The acharonim search in the Torah for a source teaching us that required sacrifices cannot be bought with sanctified money. They note that if one obligates him/herself to bring an offering and s/he is already obligated to bring an offering (sin/guilt), we would assume that the obligation cannot be fulfilled using sanctified money.
Steinsaltz teaches us that Rav Shlomo Zalman Lifshitz agrees with Rambam: once an animal has been bought to be a sacrifice using second tithe money, the holiness of the money disappears and is replaced with the new sanctity of the sacrifice. Perhaps other sacrifices could remove that sanctity as well? The Pesach offering would teach that this is not the case.