I was pondering this some more, and I think the logic behind the current interface is this:
When we give the students their feedback, we re-display the question so they can see the what they did that they are getting feedback on. This is good. Also, when re-display what they did, we make it look as close as possible to how it looked when they were answering. E.g. in a matching question we show their choices in a disabled select drop-down menu, and in a short-answer question, we display their response in a disabled text-entry box. We could just display the answer they gave in plain text, but that would only weaken the feedback loop.
So far, so good. However, we now have to consider: Is pressing the Check button part of "solving the question and inputting your answer", or is it just "signalling to Moodle that you have finished answering and want your feedback now"?
The way things currently work follows the first of those views. However, As far as I recall, that detail was not thought about in depth. I just happened that way. Now that I do think about it, the second choice is better. Therefore we should hide the check button when not needed, rather than disabling it.
Or, perhaps I am over-thinking this.
I am still interested to hear more opinions from other people. Thanks.