I don't think Shuttle's issue was that the material science wasn't there. The issue was the way the design was constrained, and the general aerospace culture at the time (that only began to change with "New Space").
Shuttle's heatshield would've been much less dangerous if it wasn't facing a giant ice and insulation covered external tank (like, if it was mounted on top of a booster), but the Air Force's demand for crossrange forced giant wings, which forced the lower mounting position.
They could've iterated on heat shield designs, particularly with attachment mechanisms, but every mission had to carry people, so you couldn't risk it, and anyway, the industry culture was already set in the "even the simplest things must cost large amounts of money and time" stage.
One of the key points that I feel a lot of people miss is that Starship is pretty much the first program actually doing the flight testing needed to understand the engineering requirements for an efficient fully reusable heatshield. They don't have much prior art to look at for tile spacing, mounting mechanisms, metal tiles or transpiration cooling. The fundamental materials haven't changed a lot, but we can see over test flights that SpaceX are figuring things out.
In the early days they used to lose tiles all the time, even after just pressure testing IIRC. Nowadays they may barely lose any tiles on static fire tests. Similarly, tile loss on reentry has decreased greatly, and we've gone from seeing plasma leaving the fins barely attached, to the latest test, where the fins were pretty much fully intact.