A bit late to the discussion, but TRs are a super awesome addition to the game. I remember back when BW2 / ORAS were about to come out, one of the things I was most hyped for was the new movepool additions certain Pokemon got, specifically new ones. Having TRs from the get go is super great because the new Pokemon don't have to deal with having sub-optimal movesets during the start of the generation. ! like how they are balanced to be limited-use as well since the moves are generally much stronger than the regular TMs barring a few exception
Regarding the moves themselves, there is a lot of good stuff. Here are my thoughts on a few of the new TM / TR moves
Mystical Fire: Ghost- and Psychic-types that don't get Flamethrower / Fire Blast would likely make pretty good users for some coverage against Steel-types. Hell, I could see normal Fire-types using this move too just because a guaranteed -1 Special Attack Drop is really powerful.
Razor Shell: This move is likely to have much lower distribution that Liquidation / Waterfall, so I doubt many Pokemon would run this. Still it would be an awesome addition to some Pokemon with shells, like Crustle,
Whirpool / Sand Tomb: Trapping moves like these have fascinated me ever since they got buffed in gen 6. While I doubt these moves will see any mainstream competitive use, they'll be a nice niche option to have on certain Pokemon.
Icicle Spear / Rock Blast: Love multi-hit moves, but outside of Pokemon with skill link or technician, I doubt anything will run these moves over stronger, more reliable options. On a side note, I'm crossing my fingers that Falinks gets Skill Link and learns these moves so it can distinguish itself from other Fighting-types.
Baton Pass: Despite Baton Pass being banned under Smogon's ruleset, I see this as a pretty fun option to abuse in Battle Tower, casual battles, and possibly AG. Passing Baton Pass boost to a relatively weak Pokemon is always really fun haha. With several setup moves as TM/TR moves, I feel that Baton Pass chains will be getting a boatload of new options.
Dragon Dance: DD has been a consistently good setup move throughout the generations, so seeing it become a TR is a bit worrisome for the metagame. Makes me kind of glad Garchomp isn't in the game. I'm hoping this move is distributed to slower Pokemon like the two fossil Dragons instead of fast mons since slower mons are easier to check.
Toxic Spikes: Toxic Spikes is a pretty decent entry hazard and could give more options to certain mons like Ferrothon. Depending how prominent Heavy Duty Boots are, however, it may not be as useful as it once was.
Stored Power: Pretty gimmicky move, but its a really fun gimmick. Baton Pass Teams would likely make the best use of this move, depending on how good its distribution is.
Power Whip / Leaf Blade: Having great physical Grass-type moves have wider distribution is fantastic. I'm predicting Power Whip will be mostly locked to Grass-types while Leaf Blade will have wider distribution. Assuming something like Leafeon of Rillaboom get Power Whip, it'll be a pretty nice upgrade in power compared to Leaf Blade / Drum Beating. The only Pokemon off the top of my head that I can think of that could get Leaf Blade is Aegislash, and it doesn't really benefit from it aside from hitting Hippowdon a bit harder. Still, I'm sure they'll be a lot of other Pokemon who can make great use of this move.
Close Combat: This is a fantastic move no doubt, but I don't see it being as widely distributed as Superpower. Still, several new Pokemons like Cinderace, and Ostagoon seem like feasible candidate to receive this move and they'd make fantastic use of it.
Nasty Plot: Oh boy, I'm worried about this move potentially being a bit too powerful . I know its basically a special version of Swords Dance, which has always had wide distribution, but I felt Swords Dance being widely distributed was generally balanced due to most physical attacks being weaker than Special attacks and Physical Attackers being vulnerable to Burn. Outside of Unaware, I don't know how teams are suppose to deal with ridiculously fast Pokemon like Dragapult spamming +2 Shadow Balls (assuming it get the Nasty Plot that is), especially with Blissey gone. I may be overreacting given that the new metagame has several decent special walls like Clefable and Tyranitar, but this move might push certain Pokemon over the edge.