It's not just cost-savings. Carbon-carbon is also much heavier... up to 10 times heavier. Furthermore, do remember that what brought Columbia down was impact on the Carbon-Carbon leading edge.
The options for the shuttle heat shield mostly revolved around "hot structure" using titanium and other refractory metals, which would have been incredibly heavy if it was to take the load, so it wasn't seen as a viable option. They tried an ablative coating on the X-15 and it turned out to be quite hard to maintain in a reusable craft. So the decision was mostly ablatives vs. tiles. It looked, at the time, like they could use tiles and then retreat to ablatives if the tiles turned out not to work.
I tend to be a believer in the "low-density reentry" idea, which got nixed after they ran out of money to make it fully re-usable. See, the less dense the craft re-entering, the less the thermal protection system needs to work. If the orbiter and external tank were combined, the thermal load is reduced. Maybe hot structures could be used in that case.
Note that SpaceX uses hot structure niobium nozzles in the upper stage. This is for a good reason. Regenerative nozzles are expensive and heavy. Carbon-carbon nozzles shatter. Whereas niobium nozzles can be smacked against the upper stage if the staging isn't smooth enough and it mostly works OK (of course, when that happened, tank sloshing ruined the mission anyway... but it would have been fine with just a good smack to the nozzle.