In Egypt case, the new capital looks to be too close to Cairo to give this sort of protection.
Brazil changed the capital for that purpose too, and made it masterfully:
Brazil had two previous capitals, the first is in Salvador, the capital was there for foreign military reasons: The city is a natural fortress, to attack Salvador by sea you need to navigate inside a bay that has cannons on both sides of the entrance, and the coast is VERY high (Salvador major landmark is a elevator, that take people from the coast to the city proper... obviously a invader army cannot use said elevator, it was deliberately designed to not support an army).
Later it was moved to Rio de Janeiro, because Rio de Janeiro was the new focus of economic activity, mostly for agricultural reasons (Brazil southeast is much more fertile than northeast, also in southeast countryside you could mine gold).
Currently, São Paulo-Rio Megalopolis has 40 million people (out of 200 million on the whole country), crammed in 0.5% of the country territory.
And precisely to avoid this, the capital now is Brasília, Brasília is in the middle of nowhere, to get there by road you cross hundreds and hundreds of kilometers of roads bordered by forests, tiny villages and farms, the only actual "reasonable" way to get in or out of Brasília is by plane, in fact when Brasília was first built, all construction materials that could not be gathered on-site had to be shipped by plane.
And the city itself was designed in a way that the population cannot take over, the government buildings are wide apart, there are lots of sniper spots on said buildings (ie: defenders can snipe attackers easily), and it also allows tanks to roll around as necessary.
We have unrest here in Brazil, tomorrow, I expect many thousands to take the streets to try to topple the government (most of the protesters want impeachment, but many want outright army coup, even civil war is necessary), but all of those people will be in São Paulo and Rio de Janeiro...
The government will be sitting safely in the capital, the president even called all ministers to the capital to wait, and the federal government has a separate defense militia (we have federal police, armed forces, and the "National Guard", the "National Guard" does not obey the defense minister, neither the police hieararchy, and is directly under the president, also the "National Guard" people can easily rally and wait in the capital, their numbers are only enough to defende the capital, many of their members are government supporters, and the army suspect that the National Guard was created precisely to counter the army itself.
Regarding Brazil... but on the other hand, Niemeyer's Brasilia ended up being a place completely pedestrian-unfriendly, full of red dust, and generally speaking, not a desirable place to live. Sure, lots of federal employees live there, and take those jobs because they pay well and offer incredible security, but the wealthy who work in Brasilia typically reside in SP or Rio and just fly in to Brasilia Mon-Thurs or similar... including the politicians. They may have succeeded in designing a city that was strategically defensible, but if everyone who matters is mostly in Rio or SP anyway, ....
A successful dictator is someone who can manipulate the masses of pedestrians to rush on the palace... to cheer the leader (and to stomp on whatever political enemy the dictator has). A dictator who has to hide from the people is a poor dictator, and the life expectancy of such a regime tend to be short.
Yeah, this is the part of the argument I don't understand... why do you need to control the government buildings? Just declare new ones. It's the guns that you need to control to own a country.
You need to arrest the old government and hold control of government buildings, because this will sway bureaucracy (both civil, police and army) on your side.
If you are interested in details, you should read "Coup d'État: A Practical Handbook" by Edward Luttwak.
Well, if the guns are controlled in the capital, how you control them yourself?
Many revolutions that worked, worked because the people in the capital physically wrested control, power is a funny thing, many people that have real power (example: the army soldiers, that actually have the guns with them), prefer the status quo unless it is very clear something changed (example, the soldiers might obey some rebels if the rebels kill and replace part of the chain of command).
But it works the other way, too. The soldiers might obey the current regime more faithfully (or at least more fearfully) if the government sits right behind their back and order them to murder people or be murdered themselves.
In any case, I seriously doubt any armed revolution would happen in Brazil anytime soon. It seems the nation has held popular presidential elections continuously since 1989. You can't persuade people to die on the street, when they can just wait four years and vote the man (or woman) out.
The most important institution to control in any coup is the media. I would be surprised if Brazil's big TV stations were all based in Brasilia.
In any event, I really hope (and believe) that Brazil is not on the brink of a coup or civil war. It would be insane to throw away the progress that has been made in recent decades. There should be a way to sort out the Petrobras corruption scandal without resorting to violence.
Australia's purpose-built capital city isn't militaristic in origin at all - basically when the country was federating, Melbourne and Sydney, as the largest cities, didn't want the other to be the capital and get more political power as a result. So the capital was built sort-of-maybe halfway between.
Washington was similar... though rather than cities it was regions that struck the power balance. The previous capitals (New York and Philadelphia) were too far in the northern region.
The idea that Brasília was designed to stop a popular revolution is a myth, just that. I lived there for close to a decade, and my mother was working in the government during its construction. At one point I tried to find any reference to this somewhat popular idea (amongst leftists, mostly), and I couldn't find anything. I talked to people involved in the architectural planning, and everyone pretty much laughed at the idea.
Just because a place has good sniper spots doesn't mean it was the builders' objective.
Also, many want impeachment, but many also are protesting against corruption and not impeachment, at least not yet. The people who want a military coup is a minority.
Brazil changed the capital for that purpose too, and made it masterfully:
Brazil had two previous capitals, the first is in Salvador, the capital was there for foreign military reasons: The city is a natural fortress, to attack Salvador by sea you need to navigate inside a bay that has cannons on both sides of the entrance, and the coast is VERY high (Salvador major landmark is a elevator, that take people from the coast to the city proper... obviously a invader army cannot use said elevator, it was deliberately designed to not support an army).
Later it was moved to Rio de Janeiro, because Rio de Janeiro was the new focus of economic activity, mostly for agricultural reasons (Brazil southeast is much more fertile than northeast, also in southeast countryside you could mine gold).
Currently, São Paulo-Rio Megalopolis has 40 million people (out of 200 million on the whole country), crammed in 0.5% of the country territory.
And precisely to avoid this, the capital now is Brasília, Brasília is in the middle of nowhere, to get there by road you cross hundreds and hundreds of kilometers of roads bordered by forests, tiny villages and farms, the only actual "reasonable" way to get in or out of Brasília is by plane, in fact when Brasília was first built, all construction materials that could not be gathered on-site had to be shipped by plane.
And the city itself was designed in a way that the population cannot take over, the government buildings are wide apart, there are lots of sniper spots on said buildings (ie: defenders can snipe attackers easily), and it also allows tanks to roll around as necessary.
We have unrest here in Brazil, tomorrow, I expect many thousands to take the streets to try to topple the government (most of the protesters want impeachment, but many want outright army coup, even civil war is necessary), but all of those people will be in São Paulo and Rio de Janeiro...
The government will be sitting safely in the capital, the president even called all ministers to the capital to wait, and the federal government has a separate defense militia (we have federal police, armed forces, and the "National Guard", the "National Guard" does not obey the defense minister, neither the police hieararchy, and is directly under the president, also the "National Guard" people can easily rally and wait in the capital, their numbers are only enough to defende the capital, many of their members are government supporters, and the army suspect that the National Guard was created precisely to counter the army itself.