When it comes to: "is it better to throw away the 6600 and replace it with a 5600, than keep running the 6600" I'm torn but: you probably need to use the 5600 for maybe 20 years to compensate for it's manufacturing energy cost (which is not directly linked to $ cost) and I think the 6600 might last that long with new RAM 10 years down the road, not so sure the newer 5600 motherboard and the CPU itself will make it that long becuse it was probably made to break to a larger extent.
Also the 6600 can be passively cooled in the Streacom case I allready have, the 5600 is to hot.
This is a little confusing because you were referring to a Core i5-6600 and presumably an i5-7500T or i7-7700T above but now you mention a 5600. Are you referring to a Ryzen 5 5600?
Yes
As we discussed elsewhere you could put the Ryzen 5 5600 into 45W ECO mode and cool it passively. Or a Ryzen 5 7600 if you decide to jump up to AM5 (which is probably a good idea even though you'll need new RAM).
As I probably replied there too I do not want to build hardware that can burn my house down if the wares are crap and decide to reset for some reason.
It will simply throttle.
Which is not good for longevity.