It could just be a case by case thing. I always had the impression that the Tower Tycoons Anabel and Palmer were the true bosses of the frontiers and I could see them being Champion level while everyone else is E4 or under tier. I certainly can't imagine the Factory Heads being that strong in traditional battles.
Outside of the frontiers, there's Red and Blue being called to Alola to manage the Battle Tree and Leon managing the Galar Battle Tower, so there's precedent for confirmed Champion level trainers leading a facility.
The Chatelaines in ORAS were also implied to be on Steven's level by Sydney, though ironically Drake in Emerald seems kind of dismissive of the BF, pic related.
>>54742055And also this.
So my best guess is that the Battle Tower and its clones are headed by Champion level trainers but everything else is too gimmicky to qualify.
