Can the entire Windows registry be copied to a new copy of Windows?

No this will not work

You would have to reinstall the softwares on a new OS

Also just overwriting registry from one OS installation to another will corrupt the destination so that defeats the purpose

Windows simply wasn't designed with this sort of usage scenario in mind. I've been fighting such cases since about 1994, when I first started using Windows NT 3.51, and I don't think I've ever gotten any kind of naively-cloned Windows install to start up cleanly. It's why there is so much specialized Windows drive cloning software on the market. We we wouldn't need all of that if a simple disk duplication worked and the OS came with the tools you needed to do that.

The biggest thing you're going to be missing out on with your plan are permissions. Just like files on disk, every key in the registry has an ACL, but .reg files don't include security info. If you don't copy all the ACLs over, the best possible case is that you lose a bunch of security because you make all keys readable and writable by normal users. More likely, you'll end up with registry keys that the OS refuses to accept; there's an excellent chance that the OS will just blue-screen on first boot.

Then you have other details to deal with, like unique per-system and per-drive SIDs.

Bottom line, either use special cloning software or be prepared to do a lot of manual re-work.