Apparently ramen stalls also wander round blowing the same kind of trumpet (rappa), but I’ve neither seen nor heard such a thing myself.
In Turkey an endless procession of salesmen came past my flat making a selection of noises to tout their various wares. The noise made by vans offering to pick up sodai gomi (large rubbish which you would otherwise have to pay to have taken away) and election campaigning vans shows that it certainly isn’t a law against making noise that stops Japanese salesmen from doing the same. So, why only tofu?
Traditionally, tofu must be eaten on the same day, which would explain the need for a local supply. I also imagine that a tofu shop is not quite worth an actual trip to, unlike the local butchers and fishmongers which still seem to do surprisingly well. Still not sure that gets to the heart of the matter, though. My final complete guess is that making tofu is, like making ramen, something that you can do with a minimum of initial investment, therefore making it a suitable small business for someone who can afford a cart but can’t afford a shop.