Large consultancies like Tata also operate in Finland + we also have a bunch of our own consultancies that operate in this manner (their consultants are regular employees of the consultancy). Earlier when I mentioned job boards for freelancers, it is particularly these large consultancies that subcontract down to freelancers via job boards (they try to fill positions from their bench, and when they are unable, they subcontract to other consultancies or freelancers).
Nice! In the US that still happens a fair amount too but I think as the industry has developed it has become much more rare than before. Athe keyword would be "corp to corp" employment, where you as the programmer either have an LLC, s-corp, or c-corp.
But with the amount of accountant overhead and government fees you have to pay per year (including to shut down your entity when you are done), it becomes a bit pointless and there aren't really magical tax savings to achieve that I know of unless you are like, really good at deducting things and surviving IRS audits. In any case, it is rare for corporations to even offer it, but maybe in some super niche areas I'm not aware of, there could be good advantages.
Still I think the hardest part is making and maintaining quality connections with people who value your skills :)