I sincerely hope that the amount of restrictions that need to be placed on the game is minimal, in an ideal case, none, for a good battling environment. Indeed literally almost every puppet in this game has some sort of 'unfairness' built into it, something that allows that puppet to break the rules as it were and soak up more damage, deal more damage, be faster, and so on than a puppet would usually be in some circumstance. It is not really a question of whether something can get an advantage in some situation, but rather the following more 'meta'-oriented questions:
1) Is the unfairness pronounced enough?
2) Is the amount of resources required to allocate to the strategy low?
3) Does the one gimmick require highly specific counter strategy from the opponent?
4) Is the unfairness rather unique and come from one ability, puppet, move, etc. combination?
5) Would the competitive game, with this one thing removed, actually become more diverse instead of less diverse?
If the answer to most of these questions is 'yes', that puppet, move, whatever is something suspect.
Some explanation of the finer points:
2) Some strategies will obviously net you benefits, such as a weather team or a baton pass team. The thing is such a team will be less equipped to deal with general threats because the large amount of requirements to execute the strategy, and thus such a strategy netting greater returns in return would be a fine gambit to take, even necessary for such a specific thing to be a viable strategy. When something that has comparable benefits yet comes from far less investment appears is where the danger lies.
3) For example, let's take that specific move that cancels weather and gets more power from it. Would the mere existence of Mary force a move slot to be such-and-such move on teams without her or be uncompetitive? This seems rather restrictive.
4) Here's a good example. There's abilities for each type that turn void moves into that type, at 130% base power. As return is a 100 power move, access to a 130 BP 100% accuracy STAB move is widespread in the puppet pool (but you do trade up your ability slot to do so). In the older Touhoumon games 'good' base power is closer to 90, so Yumeko's ability to basically have 125 BP moves seems unfair, until you realize that it's actually not that much anymore.
Side note: If there's anything I've noticed playing through the game it's this. Came to me as something of a shock, as I'd been running through the game with 60-80 base power on most of the types I had as the highest most of the time, thinking that was actually as 'good as it's going to get'. It seemed to do okay damage, but you can tell I was a bit surprised by finding out it's this much more about offense. Bit disappointed to be honest, as the wide array of support moves might see little use and we just get attack move or switch all the time. I guess when my full defense Yuyuko started to get oneshot by x2 effective things was when I noticed my opponents might be using some stuff with more 'oomph' to it (which I got later on, but was then hidden under roses and in caves and whatnot in skill cards that are hard to find)
5) This actually is the best criterion by far. E.g. take original pokemon. Start competitive battling. First thing you notice: 99% of good teams run Mewtwo, other psychic types see very little use, except for Mr. Mime. Remove Mewtwo, and you see usage of Alakazam, Gengar, and Hypno (in order of popularity) happen. In a very simple sense, the amount of actual 'options' afforded to the players is increased, and each has its pros and cons, it enriches the game. In the very other extreme, if we removed everything except Magikarp (because everything else is so much better than it), this would drastically 'reduce' the diversity, we removed too much. Not removing mewtwo, we definitely removed 'too little'.
Please go ahead and experiment, see if you can come up with some crazy shenanigans that are really hard to deal with properly.
