But in WYSIWYG editors, you can only search for raw text correct? For instance, if I want to search for all bold text, its trivial to do so using a markup language, but I don't think there is really a way to do that with conventional word processors.
It is possible to do it in word processors. LibreOffice Writer, for example, has a way to search for formatting and miscellaneous attributes, paragraph styles, and it supports regex search too.
You use the style system built into the word processor. Then when you change the style, it changes all other instances of it. You can also trivially add new styles as you need.
In Microsoft Word for Windows it's the "Styles" bar, and on MacOS it's the "Styles Pane".
It requires huge discipline to use styles properly all the time, because the options to just tweak your formatting "a little" are made more prominent in every WYSIWYG word processor I've used. And if you have to collaborate on a document with others, no chance at all.
It would be interesting to see a word processor that enforced style usage...
Actually, ever since introduction of the Ribbon in Office 2007 I found the styles to be much more prominent than the presentational formatting. Not that it stops anyone who doesn't want to learn how to use Word properly to still use the latter, but simply by size and visual importance in the UI styles are far more into your face than the other formatting options.
And sure, it takes some discipline to use styles, but that goes for any other option as well (apart from things like Docbook maybe). You're supposed to use \em in LaTeX instead of \textit for the same reasons you're supposed to use an Emphasis style in Word instead of italic text. The only difference is that the mechanism is the same in LaTeX (type a few characters – which is pretty much why for any given macro you'd be hard-pressed to actually decide whether it's semantic or presentational), while in Word it's a separate feature.