clearly, all those years of web developing have saved you from seeing any problems, which actually do require a huge ugly block of code to solve... #region is handy if you have such a block of code, and with MSVS its neatly wrapped into the ide so you just select the area and choose to outline it.
generally i am in favour of splitting things out into seperate files, however once it gets down to the one method level, i think its pretty silly to split it into more procedures/functions just for the sake of keeping it in smaller chunks. sure you /can/ wrap it into lots of little procedures, but i'm not a fan, as it breaks the ability to read the whole code in sequence without swapping files, or moving around in a large file.
at the end of the day if you want to see what is in the region, you expand it... i really fail to see the big deal there as encapsulating things in procedures has precisely the same problems in terms of maintainability and readability which have been described in the article for regions, except for that nebulous point about it being like a glorified comment... if anything its slightly worse because you can't expand the procedure in place to see its precise effect, but need to use some (implicitly error prone) thinking to substitute variables and remember things between two different files etc...
can anyone remember the early visual basics btw? they had this awesome feature where by you looked at one procedure at a time in the editor, even though they all came from the same file. its a shame they dropped it in vb 5 or 6 (can't remember which). i think that old feature is a much, MUCH, better solution than what we currently have in the more recent visual studio products.