If all the parishioners were to figure out how to make the envelopes stop coming in the mail, the parish would go broke.

But you are right, a few envelopes are better than nothing for knowing the person exists at a distant parish.
I’ve never been in a parish where they mailed out the envelopes. Even back in the 50s when I was a kid I remember someone sitting in the sacristy after Mass giving out packets and recording the numbers.
I look at who gave last year, make up envelopes for those who’ve given more than the cost of a packet (I’ve seen years when an envelope owner has only given $2) and place them at the back of the church where parishioners pick them up. There’s always a sign up sheet for people to request a packet if they’ve never used before, are new to the parish or simply want to start using them again.
The type of crazy you mention is not too far from home. On these very forums I read a Catholic reporting that if she was going to be away from her local parish for mass that weekend, she would need to have the parish priest where she did attend mass sign the weekly bulletin for that parish to say that she had in fact gone to a mass somewhere. This was so she could prove attendance for her child to be eligible for first communion. I searched out
that thread and it is still there. Puzzleannie said on that thread that the practice of taking attendance like that is disallowed in her diocese.
I have seen that in a parish where the priest wanted parents to have attended Mass for at least 6 months before having a child baptized.