Good for them. I can imagine this being extremely useful to people looking for a place to work for an hour or two between meetings or whatever. I’m sure it’s not perfect—there are schools on here and schools aren’t about to just open up their doors—but it’s a great resource.
The District could make this even better by heavily advertising it and then just sticking some folding chairs in the usually fairly empty lobbies of these buildings. You’d create an interesting 21st century public space and more importantly, a good draw. For a bit of extra work, they could even map all the private institutions with hotspots you’re able to use, maybe charge a few bucks for advertising and really be offering a valuable tool (note: this probably exists in some form, but putting it under the District’s name is how you get that branding effect). It’s not citywide wireless, a goal that D.C. should look into, but it’s a good way to, at low cost, help brand D.C. as more of a tech leader.