Is not a phrase you should use lightly... government involvement in anything is rife for mismanagement. At its reduction, a domain name is an agreement between people to use X address for Y purpose. What would this power even mean?
The entire internet was built on public funds. The very reason why Verisign has exclusive control over .com and .net is a 1993 contract [1] with the National Science Foundation (or rather InterNIC [2], the successor of Defense Data Network NIC and predecessor of ICANN). They gave them this monopoly on the condition they pay 30% into a public fund, but the court ruled it an illegal tax.
Do they add any extra value, aside from hijacking DNS with their ad pages [0]? Do they have any meaningful competitors? Can you make your own TLD and enter this market? What would be different if ICANN managed domain registrations itself, without the intermediary, short of having more checks and balances stopping them from milking their customers dry? Your government didn't need to sell all public roads to a monopoly to figure out how to tax them.
[2] https://en.wikipedia.org/wiki/InterNIC