Privacy vise this is an issue and the reason that messangers like signal and matrix would use their own services on android. However this reduced battery runtime by a good margin and android and ios get more aggressiv at killing background tasks each os iteration.
To make things worse, push notifications for matrix and signal where unrealiable, because manufacturers like oneplus, oppo and some others where killing all the background tasks against specification to win the influencer battery tests.
If regular users don’t think about these things, it’s because they’ve never thought about these ideas at all. If they did, and they are able to think, they should come to the conclusion that a 3rd party is necessary in some form.
(/s for those who need it)