I find the question as impractical as asking whether there's a core set of "people problems." Yes we have many problems to solve. And there is much overlap. But there's just too many problems one group of people might not be so great at solving that another would for it to be practical to think in terms of a core.
Languages are arguments. They're philosophies. You'll never find the one true one. And we'll never stop inventing new ones to adapt to the times and shifting circumstances. Hell, we'll invent new ones just because we're bored of speaking and/or programming that way.
IMO, the lazy principle is always a factor but it's not a Hegellian thing where we will ultimately find the one true higher language. (although I certainly hope we'll stay away from certain language mistakes so long as history remembers them). Where I hope we do evolve, however, is in properly identifying some of the really good base principles and holding on to those as things worth doing a smell-check on whenever an exception seems reasonable.
That said, don't think I'm trying to discourage you. Putting things in boxes can be a highly fruitful endeavor even if it never succeeds if you maintain awareness of the absurdity of it all. And yes, a good one to indulge in if you've got language design ambitions no doubt.