Blitz chess is already what a lot of people consider a variant. In Blitz format there are strategies and tricks that are outright blunders in longer time controls.
The biggest improvement by far for a casual player (at stage where you have some higher chess concepts understood) is to memorise.
Memorise and understand principles of openings lines (lines you want to play as white - few, more in depth, and most common lines you see being played - more, less in depth as black)
Memorise mating patters, there are certain setups that occur on board, knowing them can help playing them when they happen, or better angling to set them up yourself.
This was what made me drop chess as a teen. High level chess is a looot about memorisation. And that was when magic of chess disappeared for me :/
As a counterpoint to what you said, going back through your own game might not show you why and where you made a root cause mistake. If you dont have a background knowledge you will not know what to look for. And its rather a surface glance that you will 'get and forget' as soon as you start next game.
Better approach would be to study the positions you played after you are done playing for the day, or coming back to them on some other day.
I'm 47 and started playing around 5 years ago. I only play Blitz and Bullet because I find it fun. In the first two years I went from around 1000 on lichess to around 1700. I've been "stuck" at 1700 plus or minus 100 since then.
I know I could improve with puzzles and classical time controls and study and analysis but I have no interest in that. I play games for fun. If I improve then great. If not no problem. It's the same as breaking out a game of Tetris or something for 5 minutes to me.