Baruch she'Kivanta! This is an excellent question and it is asked by the Rishonim.

1. The Teshuvos ha'Rashba #71 (cited by the Mishnah Berurah in Sha'ar ha'Tziyun OC 446:6) writes that, on the contrary, there is proof for this opinion from the Gemara concerning Rebbi Akiva. The Gemara (beginning on 5b) states that we learn three things from Rebbi Akiva's statement. One of them is that we do not say that since burning on Yom Tov is permitted l'Tzorech it is also permitted when not l'Tzorech.

The Rashba writes that since the Halachah does not follow Rebbi Akiva on this point (since the above opinion is that of Beis Shamai in Beitzah 12a, while Beis Hillel maintains that burning is permitted on Yom Tov when not l'Tzorech), it follows that it is also permitted to burn the Chametz on Yom Tov if one forgot to do Bitul.

2. However, other Rishonim actually cite a proof from Rebbi Akiva that the Halachah does not follow the opinion of the Ran. The Maharam Chalavah writes that it is probable that the opinion of Rebbi Akiva is not inconsistent with the Halachah, since how is it possible that Rebbi Akiva would abandon the opinion of Beis Hillel and side with Beis Shamai? Therefore, we must say that Rebbi Akiva permits burning only when there is Tzorech for the day.

The Nit'ei Gavriel, by Rav Gavriel Tzinner shlit'a of New York, writes (in his notes on the Maharam Chalavah) that this may be explained based on the opinion of Tosfos later (end of 29b) in the name of the RI that if one keeps Chametz in one's house on Pesach with the intention of burning it later, one does not transgress Bal Yera'eh. Therefore, if he waits until Motza'i Yom Tov before burning it, he does not transgress Bal Yera'eh. It follows that there is no need, and therefore no Heter, to burn it on Yom Tov.

Kol Tuv,

Dovid Bloom