Paying for passage might be cheap in the short term. But paying the Danegeld is always expensive in the long term.
It might be cost effective in the short term to wait for now, but this isn't a principled stand, it's a purely pragmatic one. There is value in establishing a precedent that combatants don't get to shut down shipping for everyone else. If Europe doesn't want to establish that precedent, that's short sighted, and it green lights the Houthis to control the Red Sea. If they want to wait a bit for Iran's military capability to be further degraded so that they can establish that principle at a lower price in the near future, that might make sense.
I'm not sure what anti-ship missile capabilities Iran still even has at this point. It seems like most of the ships hit so far were hit by drones, though the reporting isn't always clear. Large military ships are going to be largely immune to Shahed drone attacks, any close-in air defense system should be able to take them out easily.