I know how does Cask works and all the benefits I can get when using it in a brand new system, but what I want to know and I don't seem to find and answer anywhere is... would it be a good idea if I delete my previous installed software and replace them with cask versions? would I see some kind of improvement, or would it be a waste of time?
There's no real advantage to reinstalling existing binaries using homebrew-cask. It's strictly a workflow improvement for when you need to install various softwares. For instance, if you wanted to have a script to install all your regularly used binaries on a new computer, that would be more efficient than manually visiting several sites and downloading, installing, etc.