I care... but the convenience of a webmail client accessible on any device is just so great. But there's no good way to really have secure end-to-end encryption in a webmail client. That's about the only thing that would make me seriously consider a desktop client.

Really, I'm not sure what the audience size is for email you can't see on your phone though.

Evolution somehow stores a cookie or can log in via webbrowser or something like that. Evolution will never get you logged out of your Gmail account (yes, I have one that I use for some things). I travel a lot and Thunderbird will always get blocked by Gmail (Please log-in via Webbrowser to confirm your identity).