Is it worth taking care of anonymity too much, even if I won't be using cryptos for any illegal matters?
Of course it is. Privacy should be a fundamental human right, and you shouldn't be willing to give it up just for the sake of convenience. I also do nothing illegal with my bitcoin, but I am still very careful and very strict with my privacy. Almost everyone in the world is strict with their privacy in some form or another, but for some reason all sense goes out the window when it comes to sending KYC documents to complete strangers online.
The argument that you don't need privacy if you aren't doing anything illegal is also known as the "nothing to hide, nothing to fear" argument. Essentially it says if you aren't doing anything wrong, then you have nothing to worry about if everybody and their aunt sticks their nose in to your personal and private information. Which is of course utter nonsense. If you have nothing to fear, then why not post under your real name? Why not share your real address and phone number? Why not share your email addresses and their passwords? Why not share your cloud storage accounts and their passwords? Why do even have curtains on your windows? Why do even wear clothes? After all, you've got nothing to hide, right?
Nonsense. It doesn't matter whether or not you have anything to hide or whether or not you are doing anything illegal. Privacy is a basic right, and you should protect it.
You might want to have a read of this topic, and my reply to it, for some more information:
https://bitcointalk.org/index.php?topic=5214200.0