I care quite a lot about what I catch my party Pokemon in, so much so that in one of my playthroughs of Scarlet, I traveled all over the map with just my basic low-level starter (even going out of bounds to leave the tutorial section early) just so I could find the special Pokeballs I wanted so I could get my preplanned team together as early as possible.
I also really care when it comes to legendaries, so much so that I soft-reset the Gen 9 encounter with Solgaleo for hours just so I could catch it in a Beast Ball lol, which, for those that don't know, has one of the worst catchrates among all the different Pokeball types. I'm fairly certain that I would have had a better chance of catching it in a basic Pokeball at full health with no statuses than I did with the Beast Ball with the best odds possible, but I can't find the site I used for calculating the catching odds to check this again, sadly.
I don't generally care if it's just Dex fillers though, but sometimes I still do lol.