If govts actually introduced crypto, it would be completely isolated from existing ecosystems. Unlike other players, govts. (western specifically) have a mandate to protect user privacy on their systems.

I believe some crypto currencies provide privacy(i.e monero) so a gov fork could work.

Currently most of the governments share the data with various corporations(usually US based such as Visa and Mastercard, SWIFT, plus various national or foreign banks) and US gov agencies so the level of privacy is not that great.

Crypto currencies could also provide transparency and open protocols so I believe a gov backed crypto would be successful in many areas(i.e public procurement)