delericho
Legend
Although I have to wonder--is it too radical a notion to not ask people what they think the core races and classes should be, but instead ask what races and classes that they've played, and base the core races and classes of the "new iteration" on the results of that poll?
WotC already pretty much have that data, through the DDI. According to Klaus over on Circvs Maximvs, Humans are by far the most played race, followed by Elves and the Dwarves. He doesn't go beyond that, save to note that those are the overwhelming favourites.
However, I (mostly) agree with you: the game should include Humans, Elves, Dwarves and Halflings regardless; if it goes beyond the 'classic 4' in the Core, then it should base those selected purely on actual popularity.
Wouldn't that kind of support my desire for twenty(-ish) classes in Core?
That point, in isolation, does. In a perfect world, the PHB would have enough room for dozens of fully-detailed classes.
However, if the choice is "twenty bare-bones classes" or "eight fully-detailed" classes, then my preference is the latter - I want to be able to play "Core Rules Only" without feeling overly limited. I want "less, done well" rather than "more sketched out". YMMV, of course.

I think the problem with 4E was the classes that didn't have roots in fantasy archetypes. Designers have a built-in appreciation for the archetype of the Wizard, therefore they write more for it. Players have a built-in appreciation for the archetype of the Wizard, therefore they select it when creating new characters, and choose to read or purchase books and articles about it.
I think it's true that some classes get better support, and I think that's because they deserve it, because some archetypes are more suitable than others. I don't think the runepriest, battlemind, warden, or seeker deserve support. However, I think the assassin, swashbuckler, psion, and scout should and would get support.
I've re-grouped these two paragraphs, as I think they go together. I think there's certainly a lot of truth in your assertion of the weakness of some of the archetypes. Conversely, I would note that while there are relatively few people playing, say, Runepriests, I think it's a good bet that for someone out there, the class was a revelation, was what they didn't know they always wanted, and instantly became their new favourite. Does that person not deserve support?
Perhaps. Or perhaps another word for scrabble is demand, which drives WotC to put effort into that support material, and results in higher quality.
They're two sides to the same coin. I did see plenty of people demanding more support for the 'minor' classes in 4e. But, due to cruel economics, they rarely got it. And so, to get decent support for their chosen classes, they had to gather together every little scrap of support they got.
It's tricky. I wouldn't really want to be in WotC's current position, since they can't please everyone. If they do decide to go with "lots of bare-bones classes", I'll certainly understand them taking that choice. It's just not my preferred way forward.