In principle I like the idea of enclosing just the router, instead of the whole machine.
However, if you enclose the whole router, heat is going to be an issue. Enclosing just the end mill may help with the screaming sound of cutting, but my router itself is uncomfortably loud, even at lower RPMs (like 20k), even when it’s not cutting anything.
Also, any air gaps are going to leak a lot of noise. If you only make slotting through cuts or carvings in flat stock it may work out, but a pocket will let out a lot of noise for example.
As for the noise of the vacuum, I think there is an easy solution. If you use a good cyclone, then I think you can use a normal vacuum cleaner. Those can be far quieter than shop vacs.