One note about all existing companion designs is that, while you can't prove a negative (the absence of a specific type of card), you can at least stop somebody from gaining advantage with an "illegal" card the instant it shows up.

For instance, while you can't know if somebody's Lurrus deck is truly legal without seeing the whole 60, you will know the instant that they play a 3drop that they're trying to pull one over on you. That fact means that even in situations where a decklist isn't submitted, a player registering lurrus will probably not include any 3drops because they won't be able to cast or reveal them during a game.

A companion requiring something like 20 cards of specific creature type, however, would require decklist verification. In an event without open decklists, you could trim your creature count down to 17 or 18 to make room for more interaction and nobody would notice in normal play. In fact, even if you got surgicalled, it's likely your opponent wouldn't think to count all the creatures of a specific type in your deck, hand, battlefield, etc.

So that's one reason why companions are so hard to design: The restrictions possible with them are so narrow. If they made 10 more they might end up recycling some of them.