I wouldn't have been surprised if this was meant to be converted to a Mario game from the beginning, as after all Miyamoto actually had more involvement with the development of DDP than SMB2J. I wouldn't have been surprised if the team was originally making a Mario game at first, then changed it into the Fuji TV ad after acquiring that deal, then changed back into a Mario game. Alright, so that was a stretch and probably didn't happen.
As for a bad idea, no it wasn't at all. Like many have said, several of the series' routes are dug into Super Mario Bros 2. If it weren't for the conversion, we wouldn't have had Shy Guys, Mario and Luigi would still be generic pallet swaps, and the trademarked weirdness of the Mario series wouldn't have gotten it's reputation (alright so SMB was pretty out there, but not nearly as much as SMB2). I think the whole "SMB2 sucks" obsession is just associated with the fact that it was so different; plus the knowledge of DDP gives haters a good excuse to bash the game. I'm not saying you have to like the game, but the appreciation of SMB2's contributions are often dismissed.