Perhaps others are right that saving fiat currencies is not the point of CBDCs, but I agree with the op that in case it is, it's not helpful. CBDCs can indeed do very little to stabilize a fiat currency, but perhaps they can help to save up on fees that banks impose on people and businesses, so there is some use to them. I'd also add that all fiat currencies are weak, pretty much. Major fiat currencies devaluated much more than they were supposed to, showing that faith in a strong Dollar or Euro is ill-founded. Russian ruble managed to become a very stable fiat currency, but at a price of Draconian controlling measures, and since the idea of linking the currency to gold was abandoned for good reason in the previous century, I wouldn't expect the current stability to be a long-term solution.
Yes, now you do not need to give fees to the bank but direct to the government. It is worse than that. It gives the government more power over its people.
CBDC is just a digital version of fiat currencies. There is no exception so there is no way it can assist in any way to a weak economy. It will create mostly an inconvenience to the majority of the population. Just think how some urban tribes in Afghanistan or Somalia will use CBDC without internet or a compatible device.