What to do if an audience member refuses to let you answer their question?
The question's title does not reveal the status of the obstructionist questioner, and this status matters enormously. Lower-status people behaving this way could not "get away with it". High-status people often can.

Given all the implicit primate-interaction and other presumption in anyone's behaving like that, in particular denying response, this should be treated like bad drivers on the highway, specifically, potentially more reactive than the indifferent bad weather or bad luck of various sorts. Namely, any substantial response, especially any expression of annoyance or umbrage, will incur a cost that makes whatever satisfaction one had hoped-for too expensive.

Instead, a dumb-happy-innocent smile and "thanks for your comment... then", to avoid engagement, is wise.

Sure, this amounts to a sort of impersonal bullying, but you yourself could not likely change the outcome. It'd require the intervention of someone of comparable status, blah-blah-blah.

So, in summary, no, such "comments" are not productive, are status-reiterating, ... and do create a generally stifling status-conscious atmosphere. Not that most human scenarios aren't status-conscious... :)