Achronim ask (see the Steipler for a nice piece): Why we don’t say that the one korban that is pasul is bateil and all the animals can be eaten?
(Even if you hold that a whole animal is a chaticha ha'reuya l'hiskabeid, that's only a din derabbanan. Here, you risk bringing chulin l'azarah on pesach sheni if bitul doesn't work and you discover the problem before zerikas ha'dam.)
The Oneg Y”T has a chiddush that tzitzis which were not spun lishma (or matzah not baked lishma) cannot become bateil if it is mixed in with other kosher threads (or good matzah). Bitul can only nullify a property of an object, e.g. a piece of meat that is assur loses that status if it falls into a mixture. Bitul cannot assign a new property to an object. The tzitzis thread (or matzah) that was not made lishma cannot attain that quality of being lishma just because it fell into a mixture.
The Mishna in Parah (9:7) tells us that if some fireplace ashes got mixed in with the ashes of parah adumah, even though the fireplace ashes are bateil to the parah adumah ashes, the mixture cannot be used to be metaheir someone. Why not? Once the ashes are bateil, shouldn’t the whole mixture be treated as parah adumah ashes, just like we treat a pot of cholent that a piece of treif meat fell into the same as a pot filled with kosher meat? The Oneg Y”T answers that this Mishna proves his yesod: meat can loses it’s status of issur through bitul, but fireplace ashes cannot attain the status of ashes of being parah adumah through bitul.
If you are the Oneg Y”T, the answer to the korban pesach question is simple: a pasul korban cannot be made into kosher hekdesh by virtue of bitul.
I wanted to share R’ Wahrman z”l's twist to this story. He suggests (Oros haPesach siman 74) that even if you reject this Oneg Y”T, there is a still a difference between bitul by korban pesach and other cases. Bitul changes halachic reality, but it cannot change physical reality. A thread of tzitzis not spun lishma is physically the same as any other thread; a matzah not baked lishma is still the same physical matzah as any other matzah. Perhaps bitul can rectify these defects, but cannot rectify a korban found to be a ba’al mum. At the end of the day, the physical reality of the blemish is still present, and it is that physical reality which prevents the korban from being accepted.