I sort of skimmed the above, so sorry if I'm misunderstanding, but you're asking why roslyn-ls would need the ability to run against different runtimes/SDKs?

I'm more familiar with omnisharp-roslyn, but I imagine they are similar. It's important that it's able to use the same compiler (roslyn) used to build whatever project it's loading. It might not be important that it runs on a particular runtime, but I guess it ensures that the runtime can load the compiler.