Interesting thread. I got to thinking it might be more doable through genetic manipulation than by way of breeding. Surely there's a gene tied to a roosters propensity to crow, but I couldn't find anything on it. If such a gene exists it might not be identified, and would take some measure, if not a lot, of time and effort to identify it. Which would of course cost money. So that might nip my whole idea in the bud.
I'm no geneticist though, I'm not even particularly in favor of genetically modified animals.
I did find a
study wherein Japanese scientist were able to link crowing to the birds circadian rhythm, not too shocking really. But the roos also responded to external stimuli, like light and sound. So altering that behavior genetically might cause the bird other problems.
Slightly unrelated, but I also found another
paper that shows how a rooster passed on mitochondrial dna to his chicks. Mitochondrial dna typically being provided by the mother. Interesting, but like I said, unrelated. I only bring it up because it got me thinking. Even if you created such a breed of crowless rooster without issue, either by breeding or genetic manipulation, you're going to encounter some restrictions as a chickenkeeper.
You would either have to only keep this crowless breed, or you wouldn't be able to breed him to the other breeds in your flock. Or at least, there's no guarantee that you would be able to keep that "crowlessness" in the line. So even if you got rid of all the cockerels you hatched, you would still need to buy a new crowless rooster eventually. If you breed him to, say, a barred rock hen, the resulting cockerels might gain their mother's breeds need/ability to crow. Even if you got one or two or more who didn't crow, and you probably would at first, every generation after that it would be less and less likely. Because you would be further diluting the crowless roosters genetics in the line.
So best case scenario, you would have to keep buying crowless roosters anyway, just like you do with your hens already. Which, in the end, I think defeats the purpose. Of course, that all depends on what your reasons for wanting one are. You could, as I said, only keep that crowless breed and retain that level of self-sufficiency, but I know very few people who only keep a single breed. Most of us enjoy some variety, I know I do.
Anyway, I'll stop rambling now. I'm just some nerd on the internet.
Might be I'm just over thinking this, and it could work out just fine, I foresee some problems, if not inconveniences, though.