You are correct that the manufacturing cost has gone up.
You are incorrect that this is the root cause of GPU prices being sky high.
If manufacturing cost was the root cause then it would be simply impossible to bring prices down without losing money.
The root cause of GPU prices being so high is lack of competition - AMD and Nvidia are choosing to maximise profit, and they are deliberately undersupplying the market to create scarcity and therefore prop up prices.
In summary, GPOU prices are ridiculously high because Nvidia and AMD are overpricing them because they believe this is what gamers will pay, NOT because manufacturing costs have forced prices to be high.
Since Intel GPUs are again TSMC manufactured, you really aren't going to see price improvements unless Intel subsidizes all of this.