As per Player's handbook, only bards and druids get access to Heat metal. Later books added forge clerics to that super-exclusive list, and UA artificers are in it too.

But why? Artificers and forge clerics makes all the sense in the world, of course. But, unless I'm missing something, bards and druids are weird choices for that list, and wizards and sorcerers are obvious choices which aren't there.

Is there an official tweet somewhere explaining the rationale behind that decision or can someone explain to me what I'm failing to see, or is it just a case of weird drunken spell-list design?

Someone on Reddit suggested the following:

A lot of people have touched on resonance, and from what I saw the response was "yes, but why the Bard in particular?"

Quite frankly, because no one else could. The wizard has the magical expertise, sure, but they don't understand the mechanics of sound like a bard does. A bard knows their instrument (and therefore their sound) better than most people know their genitalia. Anyone could know "hey, if I hit this frequency, I could energize the metal to the point that it's malleable," but not just anyone can do it. Their sounds would be too sharp, too flat, too loud, too soft, lacking the right overtones, etc., and would therefore be ineffective. Only someone with the proper blend of skills could pull this off.

TL:DR this flavor of the spell requires musical expertise, not just magical, so only the Bard can pull it off.

Okay, that sort of explains it. Except the same would apply to Shatter, which a bunch of classes have access to. And it still doesn't explain why the druid can cast Heat metal too.