> Back in the 1990s, one could buy a "double conversion" UPS that converted AC to DC then back to AC, at all times. This was, supposedly, the best type of UPS (in my experience they were also the least reliable)

They are "best" in the sense that your output is completely decoupled from your input so you got the most protection from any electrical noise. The trade-off is lower efficiency (AC-DC-AC roundtrip) and more battery wear (it's constantly 'in use').

Any >10kVA UPS is probably double-conversion/online.

If built correctly this design also suffers no transition transients. You can switch the external power off/on all day and downstream equipment will never see a glitch.