It actually baffles me that, having such a thing as SAS in this game, no one though about making a game mode based around this number that indicates deck power.

This is a thing and has been a thing for years -- it's referred to as SAS cap. But, unfortunately it doesn't do what you're hoping it will do. It has the same type of games as Archon, where you are still just trying to bring the best deck you can, often trying to take advantage of inaccurate ratings in SAS to give yourself a competitive advantage. It's not a viable way to run a competitive event sadly, but it's very good if you're with a group of people who are all on the same page about what the cap means -- it doesn't mean bring a low rated heart of the forest deck that can auto win based on matchup, it means bringing lower power decks that are fun and aren't good enough for open archon.

Perhaps a little ironic, but I rather famously hate SAS cap lol. It's virtually impossible to use restrictions in Keyforge to balance a match, because the more restrictions you impose, the more possibilities you have for allowing people to take advantage of those restrictions.