But Sonic Rumble would likely be a game that would likely not be free to buy, but not freemium either.
No, it was already planned to be free to play.
SEGA wanted its own Japanese development team to create a hit free-to-play Sonic mobile game, filling a gap where existing Sonic mobile games came from external studios (SEGA Hardlight, Gameloft, and Gamefam).
But we know that while SEGA is really succesful in Japan for their mobile games, none of these games reached same succes in Japan when they're bringing it to the west by themselves. This is why they bought Rovio.
Sonic Rumble was their fruit after they worked together with Rovio.