But a smartphone's time is set how? Via the mobile network (NITZ) or NTP (SNTP)! And what protocol is going across the Bluetooth connection but SNTP? In NTP terms, your alarm clock is now in a stratum below the smartphone, and with only one source of truth, not a good situation.
I meant the clock itself doesn’t need an internet or local network connection, with which it could do things other than syncing the time.
Given that most alarm clocks only show hours and minutes, I'm not sure micro or nano second accuracy really matters. Provided my alarm clock is within a few minutes of the correct time I don't really care.