The freedoms the free software movement tries to realize are not comparable to what you are saying. https://www.gnu.org/philosophy/free-sw.html
A way of understanding free software, IMO, is that working with software for which freedoms are socially limited (so-called proprietary software) towards someone else, the proprietor, robs the user of the software of freedom and creates some kind of social hierarchy that is undesirable.
Meanwhile, the basic idea of radical leftism is that working using capital for which freedoms are socially limited to the benefit of someone else robs the worker (really, if you think about it, user-of-capital) of freedom and creates an undesirable social hierarchy.
I think that there is some kind of parallel between both, and it's pretty interesting. That isn't to say that companies should use free software or develop free software from their self-interested point of view - as a company using free software you're almost in the same case as a worker, and as a company developing software it can align incentives to lead to better outcomes.
That being said, I'd say social democracy is an example of non-radical leftism.
I don't think that term applies at all in this context. Somewhat simplistically, Communism is 1) A viewpoint on the historical development of society, most notably the economy 2) An extrapolation from that viewpoint on where things are headed, which is judged by communists to be a bad path 3) Advocacy for a path that diverges from #2.
There's a dozen different major branches/interpretations, but at heart they are all socio-political/economic philosophies that are far more complex than simply who owns a thing.
About the only parallel I see between free software is that both want property to be owned by the community. Though even then, I'm not sure free software would have even the restrictions that might be imposed by community ownership. (The community might say "no, don't build that thing." etc.)
Perhaps in a purely communist society software would be free, but free software itself is not inherently communist.
How that relates to your argument I don't exactly know, but I guess it could be interpreted as saying that even if you admit that philosophy doesn't mean that you can't produce ""profit"" - especially if it is limited to software.
Also, in theory, you could be 100% accept communist philosophy yet operate a for profit business.
Maybe it's the HN bubble, but tech culture these days seems to have a strong element of anarcho-capitalism, taking the usual minarchism of libertarian thought just a small step further.