in the last game, black was in checkmate
in KOTH putting the king in the middle = checkmate
the 2nd game should be a draw because most stalemates occur when there is only a lone king and so that would almost remove stalemate altogether
and a lot of drawn endings would be won
In the last game black is checkmated, but not for the reason you are probably thinking, as in capture the king, in the absence of other win conditions, checkmate happens when a king is captured as opposed to just being trapped.
https://www.chess.com/variants/custom/game/28376552/1/1
For instance, in this example checkmate happened when I captured the enemy king as opposed to when I trapped the king with my queen and bishop.
If I play something similar to the last game in my first post, but with N check turned off then it ends in a draw by stalemate as I haven't captured the king and black can't move.
https://www.chess.com/variants/custom/game/28376876
While stalemate is most common with only a king left a decent fraction of stalemates occur with some blocked pawns still left on the board.
Having Bare Piece Rule vs stalemate be a draw when stalemate is a draw is selected means that a position like this
with the pawns promoting to queens, rooks, or bishops is cannot be won even with the bare piece rule.
Normally in bare piece rule, if the last non royal piece of one player is captured, and the royal piece can't recapture the game ends before the player with the bare royal piece can move.
https://www.chess.com/variants/custom/game/28371201/2/1
For instance, in this example after I captured the black rook, which was blacks last piece, the game ended, and I won, before black could move because black couldn't take back.
https://www.chess.com/variants/custom/game/28371445
In this example however, when I captured the black rook the game ended in a draw by stalemate, even though the black king was bare after I captured the rook. Being in stalemate though necessarily implies that the bare king or royal piece can't recapture, and so I think if the king or royal piece is bared at the same time as stalemate the game should just end in a win for the player to bare the enemy king regardless of what stalemate is set to.
I found that for other win conditions that when a win condition happens at the same time as stalemate, even if stalemate is set to be a draw the player who met the win condition still wins
https://www.chess.com/variants/custom/game/28371630
In this example of KOTH, for instance when I put my king in the center, even though black was not in check, couldn't move, and I had stalemate set to be a draw, because I had just met a win condition, and so it didn't matter that black was in stalemate with stalemate set to a draw.
https://www.chess.com/variants/custom/game/28371822/0/1
And in this example of capture the king, with 1 check turned on, and stalemate set to a draw, when I checked the enemy king once, I won even though black was technically in stalemate, because I had just met a win condition, and so it didn't matter that black wouldn't be able to move even without 1 check on.