WebDAV didn't really catch on, but the general product space of remote drives did. The problem with WebDAV is that like most Web* tech (and maybe Braid) it's design by committee in the abstract. To make remote drives work well for the end user requires a fairly complicated protocol with tons of ugly edge cases. The interoperable standards from committees approach tends to fail in those situations, whereas hard driving startups that use proprietary protocols they can iterate quickly tend to win.
Iteration speed > openness, when there's nothing to copy from. Standardization tends to be about bigger companies trying to commodify their competitors.
Sure you'll get people who refuse to sign up with a real phone number, that's a given. Some percentage of those people will be "thoughtful." You'll also eliminate a huge number of bots, automated signups, etc.
It's hard to argue letting all those bots on will not decrease system quality.
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I'd be very interested to hear how this can be done by an unprivileged user.
Try to race set add/removals, sure, but if it depends on the set itself getting deleted, that seems… harder.