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Outside of the castling maneuver, the pawn is the only piece for which capture and movement powers are in any way separated from each other.
Now, a philosophical chess question...

In an endgame White:RPPK vs. Black:RPK (4 total pieces to 3) that is theoretically won for White, would Black side instead have a strong chance to draw IF his rook were also allowed to move exactly one square diagonally to a vacant square? (With White's rook denied the extra mobility power.)
I think the answer is --
"No, that extra mobility is a trivial power that only helps in rare cases; capturing ability is what really matters.".

I doubt increasing the diagonal range of Black's rook to a maximum of 2 diagonal squares would change much either.
...
Black's pretend rook would however be much more powerful IF it could capture diagonally, when it was *not allowed to move diagonally* except when capturing.


I would be interested to read how others judge my conclusions; agree disagree or whichever.

Thanks.
.