"Damaged reputation" doesn't make a company go broke, debt does. Microsoft, Exxon, and many other companies have much much worse reps and are doing f*cking great.
The majority of gamers misunderstand this part of Sega history. They do remember getting burned on the 32X though. Its like the f*cking potato famine of gaming...
Sega's rep was decent enough to sell an absolute shitload of DCs at first. The DC itself, was a success. On its own, it would have been fine. In reality though it didn't exist in a vacuum, and the costs from the past were too much for the DC to overcome. The DC was killed not because it didn't move units, but because Sega needed to go 3rd party in order to make more money, and Sony, Nintendo, and MS didn't want to compete with their own console. This is what makes the "death of a platform" different now that it was in the past. The DC didn't just peter out and die, it was killed, actively, as part of a larger business strategy. The same was true of the Neo Geo Pocket and HDDVD. In the 80s formats would languish for years until it was certain the market didn't need them. Nowadays it actually doesn't matter how popular it is. A shady back room deal can kill it very quickly. HDDVD was fine one minute, selling more or less the same as BR, and then in a period of about two weeks it was f*ckING DEAD. There's never been anything (legal) like it.
So, basically, Sega sacrificed the DC to make shitty Sonic games on the Cube. The DC is the Jesus of gaming.