The government would be able to obtain a certificate identical to the one of the a website owner (the real one), enabling the mitm attack (for example with the help of ISPs etc).

Yes, but you will see that the certificate authority suddenly switches to the Hungarian government, while reading an article.

How would they get the private key? Or would this CA only allow using certs with private keys they generated instead of using CSRs?

Wouldn't Certificate Transparency make it very visible and obvious if they did that?

CT would not be allowed if ETSI does not allow it. Neither would distrusting that mis-issuing CA be allowed.