In both the games of generation 6 there were places you could go where, if you held the Circle Pad in one direction, you would go around and around forever. These places were at Lumious Tower and the battle island sandy place in ORAS.... where the Battle Mansion place is, that place, where the second day care was.... Yeah, that place. How did you feel about those places and how did you feel knowing they weren't in Sun and Moon. I loved to jam a penny or a folded piece of paper under my circle pad and letting them go in circles for ages. I liked not having to be fully present like I have to be in all other gens. After having a place dedicated to it in ORAS I thought it would come back but sadly it did not.
I said this in the discord chat, but... While, yes it did make things easier, I felt the loop areas made me lose interest in the game faster. I actually enjoy actively breeding my Pokémon. Also, I know that I didn't have to use the loop areas, I also push for using the quickest route; which happened to be using the loops. As for them not coming back, I'm happy they didn't come back. I like the little area where I can run in circles all day and make hundreds of eggs.
It was incredibly useful in X&Y and OR/AS, but now with the changes in breeding in the new games, I don't really need another place like that. On Tauros, you're able to spin in circles really easily, which is much faster, and it requires barely any attention either. I don't miss it, really.
You know I never really used them. They are cool enough but I just ran the length of the Daycare route in Kalos and in circles in my Omega Ruiby game. It doesn't bother me one bit they're not in Sun/Moon.
I do miss them, though the game has other features to help cover their absence. I wish there was an infinite lace near the nursery simply for less attention heavy breeding, but overall I think that it's loss will be tolerable.
The infinite loops were incredibly useful for me as I often had to breed lots of Pokémon (usually for other people) and I didn't want to spend all my precious time on my 3DS. So yeah, the absence of a loop in Sun/Moon is kind of a problem for me, as well as the lack of O-Powers this gen. But that's fine, I guess I'll have to stick to running around with Tauros (tho I am kinda scared of breaking my circle pad).
I never really used the loops in the previous games so it makes no difference for me. When I hatched eggs in X I would just go back and forth across the daycare route. For sun and moon I'm fine with using Tauros and either going in circles in the fence spot or just around the area. Sometimes if I get too bored with that I go to the route below the daycare and go up and down it while also smashing some of the boulders on the route (which sometimes give items which is a plus).
The only one I really used was in the Battle Resort and I don't really miss it that much tbh, it feels so much easier to hatch eggs in Gen 7.
I used the battle resort Infinity Loop extensively. But I can't say that I really miss it. Breeding on Sun and Moon seems to go by faster and feels more fun. The fact that you can just get eggs without having to dump out your current batch is way more useful than to be able to just keep on rolling.
I honestly don't mind because I used the Route in front of where the Daycare center was in X and Y. Storing up eggs in my PC, flying to Lumiose, and going back to the Pokémon Center to gather said eggs just so I can hold right on the stick wasn't worth it to me.