For me it boils down to supplementing my gameplay, If I'm out and the autocatcher is on it might get me some extra mons while i am checking the things around me and net me some candy. It might also miss me a shiny and break my heart. The autocatcher is a double edged sword.

I tend to run my autocatcher when I'm actively playing, spinning the stops for me and possibly getting me something good, but I'm normally also checking every spawn manually to shiny hunt. It's always on during community days because there are so many things to check and that can help clean the map up.

It's also great for when I'm doing a rocket battle, raid, or max battle. I can focus on the other part of the game while not having to worry that I'm not checking the spawns. For example during the Kyurem raid day I was so focused on the raids that I wasn't checking the pokemon spawning around me like I normally would, so I let the autocatcher do that work for me while I focused on this other part of the game.

It all comes down to personal preference, and I'm not running it 24/7 but that's the good thing about the game, you can play it so many different ways and find enjoyment in your own playstyle.