I've been using U2F where possible for about a year, and I have a secondary Yubikey registered everywhere I have the primary registered.
I am going to be switching to a USB-C one soon, though, and it only now occurred to me that I haven't really been keeping a "list" of all the sites where I've got them registered. Right now, not a lot of sites support it so it won't be too tough to find them. But I should probably be keeping a list so I at least can be sure when I've definitely replaced registered the new Yubikey in all places the old one was registered.
That doesn't really address your question as to what happens when you lose your keys, but it's perhaps relevant that there are a few warts around replacing even keys you haven't lost.
I am going to be switching to a USB-C one soon, though, and it only now occurred to me that I haven't really been keeping a "list" of all the sites where I've got them registered. Right now, not a lot of sites support it so it won't be too tough to find them. But I should probably be keeping a list so I at least can be sure when I've definitely replaced registered the new Yubikey in all places the old one was registered.
That doesn't really address your question as to what happens when you lose your keys, but it's perhaps relevant that there are a few warts around replacing even keys you haven't lost.