I think that I would rather have Gyms; Trials are essentially the same thing, except that you don't get a sigil/token of accomplishment for the non-Grand Trials (the Z-Crystals don't count, since they are equivalent to Gyms' Technical Machine (TM) prizes, and they don't look like Badges), and the Totem Pok?mon are not under the direct ownership of the presiding Pok?mon Trainer (whereas a Gym Leader's Pok?mon would be under such ownership). So I guess Trials/Trial sites are "Gyms: with puzzles, with the Gym Leaders 'replaced, sort of' by a stat-boosted/augmented wild Pok?mon, mostly without a Badge, with Z-Crystals in place of TMs".. If one considers Trial Captains as Gym Leader analogues and Island Kahunas as the Elite 4 analogues, then League structure is also kind of changed - instead of "8 Gym Leaders, then 4 Elite Four members", the order is "1-2 Gym Leaders, then 1 Elite 4 member. Repeat that process 4 times.". It's a slightly interesting mix-up in terms of order, but I'd rather have Trial Gyms - the Pok?mon are directly under a Trainer's ownership, everyone doesn't just necessarily rip off Petalburg City Gym's mid-battle stat-boosting gimmick, and you get a symbol representing your fight (come to think of it, here it's weird how in Alola "Elite 4" give the "Badges" rather than the "Gym Leaders" XD). I like having Gyms mixed in with the overworld like Alola did, though. I also like Alola's Trial Captain order as a mix-up.
Also, if I'm not mistaken, the Totem Pok?mon implementation in Trials means that we don't get a proper "Gym Leader battle theme" analogue? Apparently, "Vs. Totem Pok?mon" is just a remix of "Vs. Wild Pok?mon (Alola)"? If so, that's another reason I'd like Gyms or Trial Gyms, since we'd get a unique Gym Leader/Trial Captain battle theme like most, if not all, of the past regions have had.
Interesting; under this perspective, that would make Alola seem underwhelming with only 7-11 "Gym Trainers" region-wide and only 4 Gym Leaders region-wide (and 4-5 "Elite 4" members (due to repeats), not including Champion/proto-Champion Kukui..?) All of the past regions at least have somewhere between 20-100 Gym Trainers region-wide, 8 Gym Leaders, and the 4 "Elite 4" members..
Despite Alola technically having an actual "Elite 4" separate from the 4 Island Kahunas, I personally considered the Trial Captains as Gym Leader analogues, and the Island Kahunas as Elite 4 analogues.. The actual Alola Elite 4 was unnecessary, in my opinion, since 3 members were lazily rehashed, and most Leagues just have one League battle against each League member (sans Kanto and its Giovanni+rival shenanigans).
Kahili is in an odd spot; without the other 3 rehashed Trainers, she seems to fall somewhere between Island Kahuna (although that would mess up the island numbering, unless you include the artificial island), Champion (Kahili fits due to being a former island challenge Champion, although I rather like Kukui referencing the Generation 1 Champion beta element of Professor Oak, plus the position ties in with him researching Pok?mon moves), and facility head/Frontier Brain level (maybe a good fit for Kahili, since she definitely has skill but her current placement is somewhat of an anomaly)..
As for what I expect in Pok?mon Ultra Sun/Ultra Moon, due to the alternate story thing, I feel like Trials will be retained from Pok?mon Sun/Moon anyway (hopefully with Stamps for the non-Grand Trials); maybe some Gyms will be present as a bonus.. I kind of hope that the unmanned Trial Site(s) (1 that was active with a Totem Pok?mon in SM, and 1 that is not active in SM but was used in the past, if I remember) will get used (maybe with Ryuki).. I feel that Trial Captain and Island Kahuna types will either be retained or mixed up. I hope that as many of the 18 currently-existing types can get used in some way (with consideration of Guzma as a type specialist who parallels the Trial Captains and Gym Leaders - as in, if he is still Team Skull's leader, his type should not conflict with the type of a Trial Captain or Island Kahuna). Somebody in the "Alola League" definitely needs to use the Ice type, since it went unused in SM.