The percentage of the board that a piece covers is not relevant for the relative values. Absolute values are meaningless.
It is true that sliders gain in value compared to leapers on larger boards. There is another effect as well: sliders that can 'stop and destroy' an isolated Pawn (like a Rook, Queen or Dragon Horse) gain strength compared to sliders that cannot (like Bishop or Nightrider). On large boards one is typically left with a scattered isolated Pawns, some of those passers. A Rook just seeks those out one by one, and then captures them. A Bishop, however, can at best stop their advance, but thenmust remain dedicated to doing so. It can then no longer effectively act against other passers. I noticed that on 12x12 boards it was very difficult to balance an end-game of R vs B with extra Pawns on the side of the Bishop. (As long as there were some Pawns on both sides, as pure R vs B gets even more drawish on large boards as it already is on 8x8.) The Rook just seemed to keep winning, no matter how many Pawns I added on the other side.
[Edit] This suggests (average) mobility might not be the dominant factor on large boards. I did some experiments with an interesting piece: AAFsW. It turns out this piece can always force mate even on a 16x16 board (in maximally 96 moves). But the average mobility of AA on 16x16 is 8.75 (same as B on 8x8!), while B on 16x16 has on average 19.7 moves. So even with the maximally 6 moves of the FsW added, AAFsW has poorer mobility than B. Yet I expect it to easily beat a Bishop in an end-game with otherwise only Pawns, because it has a 'seek-and-destroy' capablity for Pawns. When I have time I will try some such end-games on 14x14 with Fairy-Max.
The percentage of the board that a piece covers is not relevant for the relative values. Absolute values are meaningless.
It is true that sliders gain in value compared to leapers on larger boards. There is another effect as well: sliders that can 'stop and destroy' an isolated Pawn (like a Rook, Queen or Dragon Horse) gain strength compared to sliders that cannot (like Bishop or Nightrider). On large boards one is typically left with a scattered isolated Pawns, some of those passers. A Rook just seeks those out one by one, and then captures them. A Bishop, however, can at best stop their advance, but thenmust remain dedicated to doing so. It can then no longer effectively act against other passers. I noticed that on 12x12 boards it was very difficult to balance an end-game of R vs B with extra Pawns on the side of the Bishop. (As long as there were some Pawns on both sides, as pure R vs B gets even more drawish on large boards as it already is on 8x8.) The Rook just seemed to keep winning, no matter how many Pawns I added on the other side.
[Edit] This suggests (average) mobility might not be the dominant factor on large boards. I did some experiments with an interesting piece: AAFsW. It turns out this piece can always force mate even on a 16x16 board (in maximally 96 moves). But the average mobility of AA on 16x16 is 8.75 (same as B on 8x8!), while B on 16x16 has on average 19.7 moves. So even with the maximally 6 moves of the FsW added, AAFsW has poorer mobility than B. Yet I expect it to easily beat a Bishop in an end-game with otherwise only Pawns, because it has a 'seek-and-destroy' capablity for Pawns. When I have time I will try some such end-games on 14x14 with Fairy-Max.