Take care that not all of king and pawn versus king are drawn. Their result depends on relative position of kings.
Nice example of more extreme imbalance is that sometimes King+Queen vs King+Pawn is drawn - that is when pawn is on seventh rank of bishop or rook file with defending king in front of it, while attacking king is not close enough to force checkmate.
Yeah. More commonly rook endings are notoriously hard to win.
I gained a lot of rating once I started really studying the ins and outs of all the different rook and pawn vs rook endings. Because no matter what the tablebase might say, you have to be very precise with or without the pawn.
So I started getting a lot of wins out of equal positions, and got a lot better at saving a draw in bad positions.
Pawn and minor piece vs minor piece is also fraught with drawing chances, especially with bishops. Because you can just sac the piece for the pawn and there's insufficient material for mate.
Queen and pawn vs queen is basically a 3 result game at the club level. So many ways to blunder your queen. And at GM level it tends towards a draw I think. Though it's so stupidly complicated I never even tried to properly study it.
There's a famous saying in chess: "all rook endings are drawn".
Of course, this isn't actually true. But it's a useful rule of thumb to just assume it's a draw unless you're sure it's a win, because it probably is, fucking somehow.
[1] - https://en.wikipedia.org/wiki/King_and_pawn_versus_king_endg...