Although I don't think there is any web-based IDE that currently exists[1] that provides a remotely acceptable level of usability (even for web development), I buy into the dream.
I would love to code right up until 17:15, then go pick up my kid, have dinner, play with his trains or Duplo blocks, and then at 18:45 when my wife takes the kid in for his bath, be able open my laptop at the dinner table and get right back to the work I was doing, with the same code editors and test cases open, breakpoint on the same line of code, and take advantage of that 23 minutes or so by picking up right where I left off.
I used to just have a beefy workstation dialed in at my office, and do all my coding there. When I got in the zone, I'd just stay as long as I wanted.
It was having kids that broke that arrangement for me, but I can see how it could be different things for other people. The change is that I now have things I have to (and want to) do, that require me to be certain places at certain times. So being able to code anywhere, with all my state preserved, would be terrific.
It's not so much about setting up the development environment (although that is actually pretty annoying for me this week, with the 4 Macs I regularly use all being upgraded to 10.10). It's about being able to just drop what you are doing RIGHT NOW and leave that window open with the half-written line of code, not even compiling much less something you want to check in, and then picking it up again right from that spot, when you are physically somewhere else.
That's the dream anyway. The reality is that I just mostly code less these days, and do more of other things (like writing) which are actually totally portable using current technology. But I would like it if someday my dev tools could keep all my developer state in the cloud, and yet have UX as good as the leading native IDEs. We aren't there yet, though.
[1]: Haven't tried them all, of course, but I feel like I've tried enough to extrapolate about the where the state of the art currently is.