especially since you need to enable the cookie container functionality manually and you can override it by yourself
It sounds like you're picking on a strange issue to disparage .NET without any real experience in it.
And yes the HttpClient is modern. Your entire argument so far has been a single RFC issue that is labeled up-for-grabs because it's so minor and doesn't really affect anyone. Claiming the http functionality and the whole stack isn't modern because of it just doesn't add up.
If your whole reason for not using .Net Core is based around this weird and honestly unimportant edge case, all that tells me is that you have a strange bias against the framework for some other reason and looking to nitpick.