I think it’s too confusing and potentially controversial to credit captures to particular players.
Consider the standard two player game, where instead of counting captures as +1 point for the capturer, they can instead be counted as a negative point for the other player. Indeed, manual counting over a real board often just fills in territory with captures. Further, if both players play the same number of stones, counting captures is equivalent to counting stones left living on the board.
However, the biggest reason to use area scoring is to avoid the incredible complexities of resolving life and death, as would arise under territory scoring. Under area scoring, deciding upon life and death is possible by playing out an encore to actually capture all killable stones, if disputes arise. Under territory scoring, playing on to settle disputes does not work so cleanly, since playing out captures also fills one’s own territory.