It would open yet another can of worms. The GDPR explicitly calls for the possibility of anonymous usage of services, for one.
The other thing is - imagine I were a gay man living in Poland (a country that recently made europe-wide outrage headlines with "LGBT-free zones"), or in Russia where "advocating" for LGBT is a crime, or in Saudi-Arabia where you might end up literally decapitated. I could go and discuss topics regarding my sexuality on Twitter anonymously - but with a forced tie to a government ID?! I would have to fear authorities using my free speech to get me imprisoned or worse all the time!