First of all, I admire the energy you had to not only count 
all of them, but to sit down for that long and take care of them all! WOW.
I think the feature definitely tries to help the player, but yes they become awful to deal with when they take over. The main intent seems to have been to make it so you could craft stuff with flowers without destroying an entire flowering plant by doing so. So that rules out being able to pluck them up without using a shovel. If you could still run over the flower and destroy it that way, I don't know how much that would affect gameplay. I mean not even weeds die in this game so
This kinda reminds me of bamboo in NL. Bamboo plants used to reproduce infinitely, so they would similarly take over very quickly if you weren't careful to block them in, dig up the shoots every day, something. I remember having my entire plaza just full of bamboo shoot baskets. 

 Clearly the AC team learned from that. Too bad they didn't think of the similar logic for flowers. Best we can hope is they figure out a solution in the next AC. For now, transparent patterns help.