There is no rule that allows you to take a Drawback to gain a Feat.
It's not a nerf if the rules don't support it and you don't allow it.
Drawbacks are very clear:
Drawbacks are traits in reverse. Instead of granting you a boon, they grant you a negative effect, typically in particular circumstances. If you choose to take a drawback, you can take a third trait that you have access to. You are not required to take a drawback.
A couple things to note include
- that it does not mention Feats, anywhere
- you can only do this once, for a third trait
Furthermore, Traits are valued at two traits being roughly equivalent to one Feat. This isn't exactly true, but that's the valuation based on the Additional Traits feat. You'll also note, that you cannot take the Feat more than once. By this logic, if you allowed it (which is not supported by any rules), a player could take 2 Drawbacks for 1 Feat.
Side Note: Major Drawbacks are an option from 3rd party producer Rogue Genius Games. You are under no obligation to include these rules in your game. It makes no mention of doing this more than once on a character.
GM Fiat isn't a bad thing.
Don't let your problem player try to throw this in your face. The Gamemaster's primary responsibility is
arbitrate... the rules of the game
If you're Gamemastering, you get to pick which rules and non-rules apply to your game. No player gets to pick your rules. If they don't like it, then there needs to be an open discussion where you explain that 'no, you cannot give yourself bonus feats; I don't want to have to manage that many Drawbacks to actually make you pay for them, and there's no rule that says you could anyway'. If they're worried that you're trying to manage their power level... tell them yes. Yes you are, because it's your job and 1st/2nd level characters aren't supposed to have 5 Feats.