ntpwait takes "too long"

Very quickly after startup, ntpd steps the system clock. It is several minutes before ntpwait returns (indicating that the clock is fully synced). There's clearly something happening in that interval, as various things in the ntpq -p and ntptime output change. (Status changes from UNSYNC to PLL,UNSYNC to PLL,NANO. TAI offset changes from 0 to 0 to 37.)

Would it be reasonable to add a mode to ntpwait such that it considers the clock synced after the first step by ntpd? If so, what am I losing? For example, might the clock be stepped again, especially backwards?

Specifically, daemons like Dovecot do not want the time to step backwards. They are supposed to wait until after ntpwait returns. But that means that it takes 5 minutes for Dovecot to start after a reboot. I consider that excessive and would like to do something about it, if that's possible without other compromises.

This bug (about NTP Classic) may be relevant, especially the first comment: https://bugzilla.redhat.com/show_bug.cgi?id=1361382#c1