You'll still find people making the case that we have continued to specialize computer hardware for a specific language, that language being C. They kind of have a point. I see it as more symbiotic than that: C caught on in large part because its abstract machine was a good fit for real hardware†, and that real hardware is the way it is because it's a Pareto-optimal way to do computation.
Fact is that most languages don't have a semantics which could be accelerated much in hardware. Take Java for an example: it's possible to implement the JVM as a chip, but then you have a stack machine, and you can't JIT it onto a register architecture.
What we do now is make the chip as fast as we can at doing the basic things a computer needs to do, and only that (this is the essence of RISC). That offloads making programs fast to compilers, which can do a better job of it if the instructions they're working with are very basic, and have a (reasonably) predictable duration and behavior. Itanium was the last serious attempt to disprove that thesis, and also failed rather spectacularly. The Mill is the latest contender, and well, I wish them luck.
That may not be the final word though, people should keep trying the "language on a chip" approach, and some still are. I have a hunch that Erlang semantics might be a good target for hardware-specific acceleration, there should be some degrees of freedom available from knowing that data is only shared between processes via a strict ABI. And just because implementing garbage collectors in hardware didn't really pay off in the 1980s doesn't mean that it's physically impossible to have a win with that approach. I'm just sketching out why you don't see that kind of thing much these days.
† C has been described as a "portable assembly language" and that has become steadily less true. That would be a stronger reading of my statement than I intended.