That's not actually a very big effect compared to mid latitudes. The main reason to launch near the equator is because a lot of payloads go into equatorial orbits and plane changes are expensive.
From the equator you can go into any orbit equally easily (because you just wait for the earth to rotate until you’re on the desired orbital plane), but the only way to go into an equatorial orbit without a plane change is from the equator.
That’s a big effect, certainly, but the payload boost from the additional speed is still significant.
You can’t really get into any orbit equally easy when launching from the equator. The higher the inclination, the more delta v you need. For example, the Shuttle lost several thousand pounds of payload capacity when launching to the ISS compared to what it would have been able to carry to the Space Station Freedom, which would have been at an inclination matching KSC’s latitude. It’s just that the penalty is vastly worse for launching into a low-inclination orbit from high latitudes (thus why we didn’t tell the Russians to suck it and deal with an inclination better suited to KSC).
That’s a good point, the higher the inclination the more of the equatorial rotations Speed you need to cancel out. I’d still argue it gives you more flexibility overall compared to a higher latitude launch site.
It's definitely a very small effect. Equatorial launch sites are almost always preferable in terms of the launch itself, and the fact that most launch sites aren't smack on the equator is due to logistical or political issues.
Vaguely related, Baikonur is an interesting example of political issues. It's at 45.6 degrees latitude, but the minimum inclination it can reach is 51.6 degrees, because anything less would involve dropping boosters on China, and China is not enthusiastic about the idea.
From the equator you can go into any orbit equally easily (because you just wait for the earth to rotate until you’re on the desired orbital plane), but the only way to go into an equatorial orbit without a plane change is from the equator.