If there's not a financial incentive to prevent situations like this, the likelihood that YouTube will correct it is approximately nil.
The sad truth is that the parties controlling the recordings that YouTube's algos erroneously protect are probably worth more to them financially than some church that broadcasts these performances.
It isn't an unreasonable critique but there are schools of capitalism that do not like the copyright system. That isn't an inherent part of capitalism. Peak capitalism tends to ignore copyright (eg, Silicon Valley in the early glory years, or the market for movies once BitTorrent was developed).
But, to a first approximation, in a capitalist system, if $THING doesn't make money, $THING isn't going to get done at any scale which matters. There are exceptions when philosophical principles and inherent human desires (such as curiosity and artistic expression) are involved. The corollary here, in true "the market adapts" fashion, is that if $THING is done and an entity with sufficient money dislikes $THING enough, then $THING will no longer be happening. I'm not sure whether the initial statement, or the corollary is fundamentally more distasteful.