I understand why people do it; I just think the costs outweigh the relatively minor benefits. (And yes, I realize other people weigh things differently) Having a mailreader on your desktop(s) isn't a big deal. The only time it matters much, is when it's someone else's desktop, since a lot of mail clients make the initial setup somewhat of a pain in the ass. (And I get how a layman might not remember whether their server uses starttls vs ssl; I'll admit there are barriers to fast setup, where you want to ask your friend, "Hey, can I use your machine to check my email real quick?") But while maybe some people were having to borrow other peoples' PCs a lot more around the turn of the century, nowdays nearly everyone carries one in their pocket.
And across from the relatively minor benefit of webmail, is the cost: it means you can't do encryption sanely, for example. And since it doesn't have a standard interface, now Google is proposing a proprietary one, to try to do some of the things that you could do with IMAP. That's just going to lock people into gmail specifically. I get why they are doing that, but from a user's PoV, this is wastful and harmful.
Just Say No. Now that you have a smartphone, perhaps webmail is obsolete and it's time to start phasing it out. Whereever you go, there you are.