I use them, I like them.
No, I don't use it to hide anything, just to give myself a cleaner working surface to work on. I'll typically place public methods in one, private in others, if applicable event handlers in a different one and so on and so forth (precisely as in the sample code shown).
If I am working on redefining a class' public interface, I may not want to have all the private methods get in the way when I scroll through.
You want to use incremental search... sure... but what if I don't know what the heck I am looking for?
I think the point you are making has some validity to it as it relates to the tangential points you make (bloat, maybe separation of concerns somewhere in there, etc), but come on... but you have to admit it is highly religious, as in you were high on a horse and had some adrenaline flowing when you wrote this...
Not all opinions are truths, nor all of those absolute. regions have their place, here and there and some people certainly abuse and misuse them, but as much as any other tool they all step in to aid the smith feel more comfortable in the exercise of his trade.
I like them, I don't love them or swear by them, but I certainly don't mark them with the scarlet letter like you have done here.