How can it be a balk with a baserunner on if the 12 second rule only applies if the bases are empty?
So, if the pitcher refuses to pitch the ball when runners are on base it’s a balk.
If a runner is on base is there anything in the rules stopping the pitcher from making an infinite number of pickoff throws?
No, there’s not.
I think that would be covered by the same rule - unnecessary delay of game. It would be a judgement call by the umpire, since he’d have to determine that the pickoff attempts were only to wait until the relief pitcher was ready.
Sounds like they can’t, except the rules also give the umps a lot of discretion in applying the rules. So if the runner is standing on the base the umpire might say it wasn’t an attempt to retire the runner. But if the runner keeps leading off they shouldn’t be able to stop the pitcher from throwing pickoffs. Those duels are part of the game.