Improvements for PoGo

Gyms: No! Prestiging suck hard. Now gyms are boring, but with some effort, all can get their coins. In Blissey towers, i cant get often single 10 coins for days. Now im lvl 40 and have heavy Mystic dominant area, so its easy for us to make 10-20 Blissey towers and earning coins. But it could absolutely block newer red and yellow players here. I remember that hard times i had on their lvls, and wont be an asshole for them.

Gifts: Yes for random eggs, but still Alolan should have highest chance to earn. Name tag is no needed imho. And double trade im against and simply Niantic wont make it like you wrote.

Here's my thoughts.

On gyms: I don't think they'll ever bring the old system back, as the barrier to entry was too high for lower level players. Motivation decay helps with this, but if that remained in your proposed system with berries not restoring CP, gym defense would become even more of a joke than it already is. I think the gym system is stale and could use changes, but I don't think reverting back to the old towers would be a good idea. I actually do miss prestiging though!

Trading: As the previous poster mentioned, random eggs would be neat, but Alolan eggs should always have a higher chance since we can't get them anywhere else. I also don't see the purpose of the name tag thing.

PvP: giving each Mon four random moves sounds kinda terrible and invites a host of questions. Would this mean that all the TMs spent on Mons to get the moves we wanted on them were wasted? Legacy moves could be lost? Could we change the moves? TMs were introduced in order to eliminate bad moveset RNG (soooo many Dragonites with steel wing). Switching back to randomization seems like a step in the wrong direction.
Also if PvP comes with rewards, they will need to be carefully balanced and will likely be minimal/limited (example: you can only receive rewards from battling one specific trainer once per day). If you're suggesting that every win would grant 10 RC or 10k dust, people will purposely throw matches for their friends just to help them rake in easy dust/candy in copious amounts.

I can agree to most of your points. Especially the old gym system. Too bad Niantic does not want to provide a competitive game, but rather a casual noob meta where they behave like Opera to give anyone everything they want.