(For the record I'm all for eating meat, but I agree that beef is unsustainably bad for the environment compared to other animal options like poultry and eggs.)
As long as the demand for some product causes the animal to be raised, the undesirable parts will become by-products.
A competitor for leather would depress the price of animal leather, which would tend to raise the price of meat, probably disproportionately for the best cuts. Forelegs, brains, and chitterlings would go up a few cents a pound, while tongues and tenderloins would go up by dollars per pound.
That might encourage people to eat less meat, but it might also encourage them to substitute the cheaper cuts of meat--which include the skins. Rawhide soup, anyone?
If we mostly eliminate beef (in favor of artificially-grown beef, for instance, which might be a reality in 10-20 years), that'll make cowhides much, much more expensive, so people simply won't be getting leather car seats, leather coats, etc., except maybe for extremely high-end markets.
I'm assuming here that by mentioning it in the same sentence as you say beef is bad for the environment, you are talking about being for meat production on a global scale, and not just for your personal preference.