I think it would have been interesting if it turned out Mitchell gained his powers not through the ion storm (the humans just assumed it was the storm), but it was actually the Q who caused him to gain the power as a test, so that they could gauge humanity and see how much a threat humanity could be to the Q Continuum.
I think that despite John de Lancie being great in the role, Q was a directional mistake for ST:TNG. Q's inexplicable bromance with Picard was like a cross between the "deus ex machina" of an ancient Greek play and Kazoo of The Flintstones.
Kirk had his run-ins with superbeings, but none of them became a semi-regular, impishly helping and hindering Kirk's missions for sport. Q, as a vastly powerful and eternal superbeing, should never have found one particular Frenchman with a British accent so fascinating.
On the other hand, purely as an alternate universe story, it might be fun to imagine WNMHGB ending differently. Suppose after Gary bit the dust, Elizabeth had stood up, brushed herself off, and said "Good work, Captain. Let's get back to the ship."
And then she stays in Star Fleet, using her superpowers to get the Enterprise out of every jam. She could have put Kirk on equal footing with Charlie Evans, Trelane, and Apollo.
She could have captured the Romulan ship intact in "Balance of Terror." If she was in the landing party that got snatched by the Gamesters of Triskelion, she could have emancipated the slaves in two minutes and given each Provider a wicked-ass migraine headache.
It might make for lousy one-hour drama, but being her would be a blast.