Couldn’t the whole currency change be done slowly? There is a 15 years span between the Rebellion and ASOIAF. The crown could change the coins that it was getting its hands on, let both “golden dragons” and “golden stags” be equivalent and valid at the same time. Eventually dragons would’ve disappeared.

Still tricky. 

1. In order to issue enough new coins to circulate an entirely new currency, you need a lot of precious metal on hand. Even doing it over time
2. Unless you at least match the gold content of previous coins, Gresham’s Law works against you.
3. Economic dislocation is not popular and a new regime wants to avoid angering everyone in the kingdom with money.
4. It’s a huge amount of work for a really marginal gain.