Closing the Bab el Mandab is not that big of a deal. Because, as you said, ships can simply come through the Suez Canal and go back the same way. Hormuz is a real chokepoint cause there is no way out.
Paying slightly more fuel cost for shipping and going a bit more longer distance is a much better deal than not having any ability to go out.
That assumes the Suez Canal remains a safe alternative. If vessels start taking direct hits while transiting the canal, it wouldn't take many incidents for traffic to be suspended. A single disabled ship can disrupt operations & a couple of successful strikes could effectively shut the route down.
The same applies to the Bab el-Mandeb. If both ends of the Red Sea become contested, the entire corridor is effectively compromised.
On top of that, any damage to the submarine cable infrastructure in the Red Sea would have consequences far beyond shipping, affecting international telecommunications & internet connectivity as well.