The ancient style of HLL-specialized hardware no longer makes sense, but that doesn't mean that there aren't other improvements that make sense. For example, support for read and write barriers (especially read barriers) would dramatically improve garbage collection.
That's plausible, although I'm somewhat skeptical why it wouldn't have shown up in someone's hardware if it truly worked out to be worth the cost, since there is a lot of enterprise software built on the JVM and .NET that would benefit from garbage collection speedups, and which is being run by companies willing to pay for those speedups.
It did show up in somebody's hardware. Azul made (and is still making) hardware for Java that does this. They also release an x86 JVM that is able to fake it a bit by using HW virtualization support and double mapping pages.