nah, is not about the budget. It's not happening because Sega doesn't want the port, probably because good old licensing issues.
Sealth pretty much hinted about it if I'm not mistaken.
That is strange that you brought that up, as Sega doesn't fully own Sonic 1 & 2's score, but they have full rights to Sonic 3&K's score. They have to licence it out from the JP Musician they hired for Sonic 1 & 2 every time a port/version/track remix/ect releases.
With Sonic 3, they own all the music to that. Licencing might be an issue for some of the MJ Composed songs (Ice Cap, Launch Base) but I don't see that being much of an issue considering how Sega does own the rights to those songs. They own all the rights to the S&K half of the game, so that explains Sky Sanctuary appearing in Generations for example.
If I'm wrong about anything, feel free to correct me .