Should I use 'by' as a preposition of time in past/future perfect tenses only?

In that sense, you can use 'by' with any tense. Consider its meaning as given by the Longman dictionary:

Before or not later than a particular time.

Examples:

  • The document needs to be ready by next Friday.
  • By the end of the day we had sold over 2000 tickets.
  • By the time we got home we were tired and hungry.
  • I'll be home by 9:30.
  • Please try to have this done by Friday.

All the examples are borrowed from the Longman dict. so you can trust them.