Yeah, this is a good way to design a fast interpreter! It's traditionally called a "threaded interpreter", or (somewhat confusingly) "threaded code":

https://en.wikipedia.org/wiki/Threaded_code

http://www.complang.tuwien.ac.at/forth/threaded-code.html

You can see an example of this particular implementation style (where each operation is a tail call to a C function, passing the registers as arguments) at the second link above, under "continuation-passing style".

One of the big advantages of a threaded interpreter is relatively good branch prediction. A simple switch-based dispatch loop has a single indirect jump at its core, which is almost entirely unpredictable -- whereas threaded dispatch puts a copy of that indirect jump at the end of each opcode's implementation, giving the branch predictor way more data to work with. Effectively, you're letting it use the current opcode to help predict the next opcode!