I agree that competitiveness can risk intoxicating the community, but nerfing and upgrading Servants specifically for MP wouldn't be a bad idea. It'd just take a lot of additional efforts from the developers to get it all balanced out due to the enormous character roster. Subdividing PvP into several segments could also help keeping things fair between players. It's really not a case of "more is worse" If someone feels their team isn't good enough for PvP, then they can simply stick to single player!
I used to play Fairy Tail. The countless flaws aside, it had an enjoyable PvP mode despite the lack of actual player involvement during battles. I constantly ranked 2nd/3rd on the leaderboards before quitting. Now I also quit FGO due in part to lack of PvP.
It would be a really bad idea considering the people who spend hundreds or thousands of dollars getting some of those characters, i mean they would completely feel robbed if the OP team they spent so much money on isnt exactly OP anymore, just think about the NP levels and how that works, imagine someone who went the extra mile and didnt just spent a couple hundred dollars getting his waifu, but instead spent more than a thousand dollars getting her to NP5 only to later get nerfed on MP.