Losing fights sooner is an important go lesson, related to the OPs point about invasions.

The sooner you realize that you've lost a fight, the less you typically lose (early detection means lots of aji).

My favorite breakthrough when I was learning go, was the game that I crushed an opponent a stone stronger than me (or rather a stone stronger than I was before the breakthrough) by giving way at every fight, and then at the end of the middle game, destroying a formation he thought was safe with the aji created along the way. It was all about paying attention to what I could gain while giving up original aims, and how that would affect situations elsewhere on the board. For a while that became my style: winning by losing: lose every fight but win the game. That was my jump from 6k to 3k overnight.