So the plot holes can be explained by the TVA explaining that they have essentially a script for whats supposed to happen on the sacred timeline and anything that deviates from that script needs to be stopped.

So captain American going to live with Peggy is a part of the script. Doctor strange messing with the multiverse in no way home is part of the script. Also to add another layer the loki variant escaping wasn't a part of the TVAs known script so they tried to punish him but that was actually a part of he who remains script the TVA just wasn't aware of his plan. Although it's a plot device it can be used to explain all TVAs inconsistencies anything they don't interfere in is supposed to happen that way.