i was thinkin of doing that, but I thought I was crazy!
Edit: Like this, hard to tell but the finished product doesn't really look too bad?:
That's a very ingenious setup. I'd try it if I didn't know how well the router works. Can't tell anything about the finish. But think of this: Have you ever seen a band sawn surface as smooth as a routed surface?
Then too, the diameter is totally the result of the skill with which the hole is made in proximity to the blade kerf. Totally unadjustible if it's not right.
When the router setup is adjusted right, the shafts will be burnished as slick as if they were varnished.
One thing not mentioned yet is that the pivot of the arm that holds the blocks should be as close to the bit as practical. That way the far end moves much more than the input bock when you adjust the cut size.
Also, way up above, you mentioned that you are making 3/8" shafts. WHY? You can just as easily make 11/32". Veritas-type cutters are limited to the sizes the maker provides, but with the router setup, you can make any diameter you want. I have bushings for 1/4" to 23/64".
Jim