After all, it was the Avengers’ actions during the Time Heist mission at the Battle of New York that arguably led to the variant Loki escaping his fate in the Sacred Timeline.
First and foremost, the storytelling device of the Sacred Timeline basically allows Marvel Studios creators to easily sidestep any further questions about how the events of Avengers: Endgame’s Time Heist relate to Loki and the TVA.
That’s definitely a cop-out of sorts, but questions of time travel in Endgame have been rather cumbersome for Marvel to answer to fan satisfaction.
Of course, Endgame’s Time Heist being part of the Sacred Timeline doesn’t justify the fact that Steve Rogers inevitably created an entire variant timeline by staying with Peggy Carter in the 1950s after returning the Infinity Stones.
It’s possible that Cap was detained by the organization, but his service record and heroism got him a “pass” of sorts: The TVA let him live out his life with Peggy, but eventually scheduled his timeline for reset or erasure while allowing “Old Man Rogers” to go back to his native timeline.
Sure, the TVA has all kinds of impressive technology, but the rules about how they use it and what their jurisdiction is, seems like a much murkier matter.