You're right, it is subjective, but your reasoning for why it's the best is wrong. If you said something like, "Doom is the best fps of all time because there's still nothing that I find more fun." it would have been fine, but you went and said that it was the best simply because it influenced and inspired many games after it. That wouldn't make it the best, that would just make it an original game. For it to be the best fps it would need to have the best fps mechanics, which it just simply doesn't. Regardless, if we use your logic the best fps of all time would have to be Wolfenstein, simply because it was the first and inspired every single game after it.