"they'll make more working visas available "
Except a fair portion of leavers think Brexit is about cutting immigration. They'll look askance at bringing in workers unless it directly affects them - so continue to welcome doctors and nurses and medical technicians while complaining that net immigration still isn't falling. And headline rates of work visas will go up even if it's only converting EU workers to visa-ed workers.
And it's simpler for a business at a moment to bring in staff. EU national?, show the passport, job done, start Monday. Not EU? fill in forms for application. Wait, get visa, check visa then start work.