I don't agree. Free software would still be free even if copyright were to be abolished, if anything it would flourish further. That is because even proprietary software could be better integrated.

You're conflating what "Free Software" means and what Copyleft means. In any case, they both need protection from people like you who want to take it and benefit for free, without having to give anything back. Copyleft was designed specifically to prevent against people with your mindset. Permissively licensed software needs copyright to protect authorship rules, although the requirements are lessened.