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I don't think that 'one can checkmate with any piece + K vs K' is bad: it makes draws more rare!
There is a flaw with this, a P+K is more powerful than a Q+K. The Queen can never make its queen move while the pawn will either make a king move or a queen move. Also, one can checkmate with any piece + K vs K. I find it really bad that your best pieces are the most abundant...

Every move imitates the ability of the piece moved before, except the first move for nothing is before it. What if time is circular, in that spirit I propose the following variant: As a first move, any piece can be moved with any power, however this implies the last move must be made with a piece with such power, and any move during the game that would make such a ending impossible is declared illeagal.
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