This approach got a bad reputation by the late 1980s, thanks to some spectacular failures like the iAPX 432. The death of the Lisp Machine market wasn't spectacular in the same way, but they weren't a commercial success either, and contributed to the sentiment that tailoring the hardware for specific languages wasn't the way forward.
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.