You can, but if you actually start .NET on Linux without Windows and Visual Studio, you're not going to have the best experience. Lacking the background knowledge of the old .NET framework and how VS works was a consistent pain - both when reading outdated documentation and when getting help on something.
I'd recommend it to a Windows dev who wants to go crossplatform, but never to a crossplatform dev.
This is simply not true. I have developed years .NET Core C# solutions on Linux with zero friction. My choice for IDE in Linux is Jetbrains Rider, which I actually think is in many ways supperior to VS.
As someone who was encouraged as part of a merger to start looking at dotnet who was entirely Linux based previously I've found this experience to be better than I expected.
It's confusing if you have to deal with legacy applications running old versions of the frame I concur, but if you're on a greenfield project working with dotnet 5+ the experience is pretty good.
I work with vscode on nixos which is probably one of the most challenging Linux environments, and have experienced no blocks. I have had to install mono manually to work around some bugs and write a couple of patches as vscode can't write things where it wants to the read-only nature of nixos, but this is just part of the usual nixos experience.
TLDR: For me, if you're using linux and you wanna give dotnet a go, try it, you might also be pleasantly surprised.
I'd recommend it to a Windows dev who wants to go crossplatform, but never to a crossplatform dev.