Public higher-order endgame tablebases for *common* positions? It's easy for me to locate 6-piece tablebases online for free (e.g. lichess), and I know 7-piece tablebases exist (cf. Lomonosov tablebase), but I don't know of any easy way to access them.

However, I'm not really interested in all the weird positions like K4B vs KQ that a ≥7-piece tablebase would "honestly" have to include to be called as such. Haven't there been any restricted tablebases generated that only bother to include useful positions, such as e.g. KR vs. KR with more than a total of two pawns? Or is such a thing still technically infeasible?

(I realize that in theory, such a tablebase may not be 100% perfect, since calculations for common positions may be inextricably linked to those for uncommon ones; I would hope this issue could be circumvented with a minimum of resources spent brute forcing the uncommon positions and a minimum loss of accuracy for the common positions, but I could be wrong)
I understand where you are getting from. Unfortunately, it doesn't quite work like that. To generate a 7-man KRPPvKRP you would also need 7-man endgames for the promotion. You would need:


KRQPvKRP
KRQPvKRQ
KRQQvKRQ
KRBBvKRB
.......


Can you see, it's really not that easy to generate an endgame with a pawn, because that can transpose to another endgame with the same number of pieces.

We do have technology to generate Syzygy 7-piece, but you'd need a super-computer or a high-performance-computing to do it. Google can definitely do it if they want to. So far, nobody wants to cover the costs.