I mean if the pod's ready to launch and the ship's in a suitable position, why would it matter what alert status you're at?
My starting point here is that the pod was not ready to launch. In fact, ion pods virtually never are, because ion storms are such fickle beasts; one has to hunt for them, but carefully, because this places the ship at risk, and one has to launch the pod when one has the chance. But ship's safety is always paramount, and the Captain is the one to decide on that.
Thus, if the ship is only mildly endangered (yellow alert), pod preparations can proceed. If the skipper feels it's time to go, there's only a second or two to respond, so the skipper is expected to hit red alert, at which point dozens of crewmen snap to action: the pod specialist withdraws and the pod is launched as is (so that the whole risky thing hasn't been done for nothing), the helmsman wrestles the ship out of the storm, and no doubt other people do other things to protect the ship.
If the procedure at hitting red alert in an ion storm merely consisted of securing the ship, then the pod would go unlaunched and the mission would be a failure of sorts. So pod launch would be integrated to the procedure, with all the control of every aspect of the procedure on the skipper's fingertips.
Note that in TOS, yellow and red alert do not automatically correspond to things like "shields up" or "weapons hot". Those are separate commands, and situation-dependent. Probably in red alert, the crew must be ready to raise the shields immediately; in yellow alert, they need not be that prepared; etc.