Show me a team who dumped their Franchise QB so they could save money to keep their existing roster mostly intact? You speak of fantasy.
QB's don't account for 50% of the salary cap. They usually account around 15%. Moving off of him, his replacement is going to eat into that. Leaving you with about $20M in additional space to go get a really good player, but not a top flight player at the more valuable non-QB positions. As They go for $30M+.
Personal preferences are one thing, the actual data is another.
The data is clear, it's up to you if you choose to ignore it or not.
It's impossible to build a dynasty in the modern NFL, NFL rosters turnover 80% every 3 years. However, Franchise QBs are one of the few ways you can actually consistently win, as the most valuable piece on the chess board that can be a 15 yr mainstay, keeping that player intact, while moving the parts around him is the way to go. Not dumping him to save a measly 5-15% on the cap depending on the direction you go with his replacement.
According to your logic, the Chiefs were fools for paying Mahomes and should've moved off of him instead.
Belichick put out the blue-print with Brady, constantly remaking the team around him. And Brady's discounts over his career were highly exaggerated. Between Russell Wilson signing his first extension in 2015 through 2019. The Patriots won 2 more Super Bowls, while Brady counted $15M total cap dollars more ($3M avg.) against the cap in that span than Wilson. The real key to Belichick's team building success was never over paying the other guys, while continuing to redo Brady's contract to keep his cap hits as low as they could manage. (Still costed more than Wilson 2015-2019 on avg.)
The Chiefs are executing it right now as well, moving off other expensive pieces to keep their QB and it's working. They will extend Mahomes in the not too distant future, (probably next off-season) to lower his cap number, and keep pushing.