I will start by saying that I am in the camp to leave Terastillization be and play the mechanic as intended. I have been playing competitive since generation three and have seen many changes in that time, many good, many terrible.
Before I give reasons why it should not be restricted, let me say why it should not be outright banned. Unlike any previous generational gimmick, this is a mechanic that offers far more diversity for teambuilding while also testing players knowledge of individual pokemon. Unlike something like Dynamax, there are no outright stat changes. You don't magically double your Dragonites health and proceed to fire off 3 mini Z moves that boost your speed. This is a mechanic that benefits each Pokemon uniquely based on their strengths, weaknesses, and abilities. In all my games played, Terastillization is never the win button and often times can backfire on you, unlike any other mechanic before.
Reasons I am against various forms of limitations on the mechanic.
1) Revealing Tera types not only defeats the purpose of the mechanic, but flat out often tells you what that mon wants to do. This is the equivalent of allowing your opponent to be able to check your EV/IV spread mid battle, it is almost certainly blatantly unfair to one player compared to another. In the gen 6 metagame, running two or more pokemon capable of mega evolving was a big part of the metagame, which kept the opponent guessing. Your opponent had to second guess if you were running, say, defensive Swampert vs Mega Swampert. In gen 7, any mon had the ability to hold a tactical nuke and no one batted an eye at the idea that of viewing which Pokemon had a Z Crystal because that would defeat the purpose of the set. And guess what? Players could usually figure out which mon wanted to drop a Z move and which one it was because the meta game was allowed to develop and players quickly found out what worked and what didn't.
2) The Power level is no where near the heights Dynamax could reach. Dynamax was a complete game changer if you were already ahead and could allow players to come back from defeat if you were behind. Terastilization is more like a Z Move. It gets one good surprise in, but if you don't have a good opening to use it properly than your in trouble. There are obviously pokemon that can use the mechanic better than others. Some abilities also crank up the power level far higher like Adaptability, but that says more about the performance of that Pokemon in question rather than the imbalance of the mechanic. In fact, if you were to see something that blatant on the team, many should just treat it as they did a backline Mega Pokemon, with caution and respect that it is there.
3) The removal of Tera Blast. I would go so far to say as Tera Blast is a noob trap in many ways and a worse Hidden power. On paper it's an 80 BP normal attack that matches whatever your stronger damaging stat is. But in practice, the move is inherently bad if you DON"T terrastilze that pokemon. If you don't tera that pokemon, it eats up a move slot that something better could have been. When Hidden Power was around, although only 60 BP, it was never a dead weight move on a moveset. It ALWAYS provided needed coverage, which Tera Blast does not.
4) Limiting the mechanic to STAB typing only. This actually makes the mechanic much more one sided worse to deal with. In fact, I'd say this is the least competitive argument of them all. What this is actually saying is " I want my sweepers to hit harder and I want my opponents walls to block less." I want to preface this is not a defensive dynamax arguement. There are three big reasons why. The first reason is simply that this promotes greater hyper offensive play and closely mimics the exact reason Dynamax was banned. One mon gaining far more value than others simply because it has higher attack stats or it was given premature speed/attack buffs to start steamrolling. Allowing for any type tera type to be accessable by any mon keeps more powerful sweeper abusers in check and promotes options for weaker mons with unqiue niches. Second reason: This is just blatantly unfair to mons that are already monotype. Pokemon with two types get all the weaknesses and strengths of both those types, but mono type mons are still stuck with those same strengths and weaknesses with more damage output. This drastically affects tiering as inherently there are just some tera types that are ass compared to others. Tera as a mechanic is balanced by the fact that you can shift types on the fly to another type, so ostracizing a large population of monotype pokemon to favor dual types is blatantly uncompetitive. And reason three, this turns things into a very slippery slope in terms of weather and terrain. I played all throughout the gen 5 meta game, through every ban and rule change, questionable or not. Similar to my last point, damage boosting weather/terrains would undoubtable become the meta so you can essentially get your adaptability boosted grass, water, fire, electric, or psychic move off. I can further prove this to be true given the new Paradox pokemon and their sun/electric terrain based abilities. We have already seen the ban of Iron Bundle and Flutter Mane. Many of these Paradox pokemon wouldn't be the main terastilizers for their teams, but they still would retain the option to be.
5) Limiting the amount of mons that can Terastilize per team. Honestly I find this one to just be dumb and lacks any real congruency with prior meta games. As I mentioned in my argument against revealing tera types, we had no such restriction on Mega's or Z Moves. If you wanted you could run a team of fully mega evolving pokemon, but only one could actually use it. Furthermore, I have used and fought many players on ladder that had two Z move users in their team just for the option of hitting more threats.
My conclusion: From all my games on ladder and on cart, this mechanic has been the most balanced of all 4. There isn't a surprise nuke like Z moves because it is very easy too tell 90% of the time what mons are going to use it. The mechanic isn't as centralizing as Megas because there have been many games either me or my opponent hasn't needed to use the mechanic and their team didn't rely on it to function. And it is no where near the power level of dynamax. Any changes to playstyle of the mechanic like "limiting to stab only" sways the mechanic further into unbalanced territory. Seeing an opponents teratype is equivalent to knowing what items or ev/iv's your opponent has in team preview. I Believe the mechanic is far more balanced than people believe because many have not adapted to the playstyle, especially coming off a meta where Dynamax, Z Moves, and Megas were not present. I think the biggest reason we are seeing complaints on the mechanic is simply due to many players unwillingness to shift their team building outside of their comfort zone (think the Goldengo vs Corviknight argument). Lastly, I think the one thing that many forget too look at is that this is the first mechanic with a true trade off outside of individual pokemon and that by changing your pokemons type, you are also opening it up to new weaknesses as well. In fact, I think this is the only mechanic to have actual weaknesses built into it.