Well each cast burns through 24 turns and if you are extremely lucky every cast will round up 900K influence... so say you had 400 turns at hand, which is even a lot for most people:
400/24=16 if you round down
16*900,000=14,000,000
14M influence is not usually enough to take over a port. And that's if you are lucky. Say that you actually ended up with the average (550K) every cast:
16*550K=8,800,000
Again, no where near enough to take a port.
So unless 5 or more people decided to switch all at once and they had double turns storage plus they bought 200 extra turns, a port takeover would be difficult. And between the price for extra turns and the price of the turns themselves, it would actually be cheaper to just takeover a port the old-fashioned way.
A prison warden must be the very best at kung fu.