Well, there's limits on how much a given provider can order how often. Can't recall what those limits are, but it's a thing due to how long a given vaccine is stable, what the supply is from the makers, etc. I never handled that end of things, so I don't recall the exact details, only that there's a dance between how much is predicted to be needed, and actual demand.

Childhood vaccines here are rarely out, it's the seasonal ones. You might have to wait a few days, which isn't long, at most though, so driving a county over isn't something most folks do, they'll just wait, whether it's seasonal or not. I will, and have because I know to call ahead and verify what I need is available.

Since pharmacies are doing it now, it's easier. Back a while, you only got vaccines at a doctor's office, so just driving to another wasn't an option. You have to make the appointment, deal with insurance, etc. Myself, I'll take a longer drive to get everything at once rather than make multiple trips. Some folks, it's the opposite.