Really matters Depending on The state of the game and the position.
If it's The opening, Rooks and queen are Mostly useless (though can be proved wrong if you play an opening that does use the rook and queen, and is justifiable) , The pawn moves and controls central squares, as well as allow the bishop to develop, Speaking of the bishop, Bishops are equal or worse than a Knight in the opening phase, The bishop only gets better after the opening.
In the middle game, Rooks and bishops become more valuable while Knights are weaker since they don't have a nice long range attack, But if the position is closed they might be better than bishops.
Pawns in the middle game can be used to do a Pawn storm on the opponents queenside or Kingside depending on where they castle, But they mostly trade and threat.
Queens become useful, A piece that can be used to create threats from a long distance and can create tactics, Though you have to be really careful to not accidentally sacrifice your queen.
The Endgame is Where Pawns become Very valuable if you have them, sometimes they are the last Pieces on the board, You have to promote them.
King, Though can't be captured and has no point, becomes more useful in the endgame with fewer pieces to checkmate it.
Rooks, Bishops and queens become Really nice and arguably the best.
Knights are very weak since you need 3 knights just to checkmate a lone king (or 2 knights vs a pawn but that only works sometimes) , it's just not worth promoting a pawn to knight unless You see a tactic.
This could also tell that bishops are stronger than knights dually when checkmating with the king.
The King's infinite value is due to never being captured and being the main part of the whole game. If we have to find out its mobility value, then we have to think about what is the value when the king could be a capturable piece.