The case
Bugs, Daffy and Porky were the backbone of Saturday morning, and the title card said Looney Tunes every time. The series began as a vehicle for Warner Bros.' music catalog, so the pun was on "tunes" from day one.
The Toons spelling got a real foothold in 1990 with "Tiny Toon Adventures," and then "Animaniacs" and the general rise of "toon" as a word. For a generation that grew up between the two, the spellings merged.
Why our brains do this
"Toon" is the obvious word for a cartoon, and a later, related show used it. Memory promotes the version that makes more sense.
Sources: Wikipedia — Looney Tunes · Wikipedia — Tiny Toon Adventures · Wikipedia — False memory: the Mandela effect
