Like Tsuyu is a frog, Izuku's Ghost Sight Quirk is actually that he is a cat.
While he doesn't look like Officer Tamakawa, the only cat-type Quirk-user, we have seen through Tsuyu that people with animal mutation Quirks don't have to look wholly like the animal, as long as their traits reflect them.
Cats can see ghosts in the YUTS story and, while Tamakawa cannot, Izuku and Mika can. Tsuyu's family, though they all have frog-type mutation Quirks, do not all look the same, and it is likely that their Quirks do not all reflect in the same way.
A lot of parallels are drawn between Izuku and cats, especially regarding his eyes. Izuku's tapeta lucida was even edited into previous chapters.
At the very least, Izuku's Quirk is not solely that he sees ghosts, but he also has the eyes of a cat.
The fic will end with Izuku's ghost-seeing quirk erased.
Since the internship arc has already gone so differently, Mirio's quirk may survive the course of the fic, but Izuku's will be erased. What would be a more complete ending to something that follows an incomplete story than to take away the thing that makes the fic unique?