As both an experienced Windows and Linux Mint user, I have to be honest. The free alternatives are good, don't take me wrong. But I have recently switched back from Linux Mint to Windows on my desktop (still have a Linux laptop though) and it really felt like a relief. I really missed the user-friendlyness of most tools running on Windows. Including Paint.NET.
I do not like GIMP, it is overly complex and things like rendering rectangles is a breeze with Paint.NET but a hell of a task with GIMP. And what other alternatives are there? A lot, and I tried near all of them but none really fit my needs. Either they were buggy, complex like GIMP or just lacking features. And with Paint.NET you don't get those issues, it just works plain and easy.
However, I would be lying if I say that I am still using Paint.NET for my day to day tasks as I stumbled on another amazing pixelart editor here on Itch called Pixelorama. I have used it to draw sprites on Linux Mint and I even use it now to draw sprites on Windows. I only use Paint.NET when I need some more advanced editing for images but other than that, no. I don't use it.
You see, thing is.. While I absolutely support open-source, as I have some open-source projects of my own, it is also its greatest disadvantage. Everyone can take the source, adjust it to their needs, compile another version of it and publish it. And as a result you will get like 100 versions of the same software. And at a certain point finding the right software becomes a needle in a haystack. So yes, there are good open-source alternatives out there but I agree with dulsi here, you probably won't be as productive. And it is for that reason why I switched back to Windows.