Could/would CBDCs be listed on any exchanges?

Forgive the ignorance for the lack of knowledge about how CBDCs work (there's probably not many that would), but as the question asks, would this happen? I don't mean just crypto exchanges, any kind of exchange, does it's status as a digital money (not crypto), would it be possible to trade it, like we can trade our current money on exchanges for commodities and securities?

If this is possible, I wonder if that will be super bullish. Because a lot of people don't put their money into crypto, because the fact of having to on-ramp your fiat into exchanges of any kind is the first roadblock of Crypto adaption. Much like ETFs can expose investors to BTC and ETH, is it possible that using an already digital currency that can be exchanged on an exchange, and with some exchanges and services hosting crypto (ever increasingly) it will be very easy to trade for crypto since you have money in the 'eco-system'.

But maybe this is also just day dreaming and the government will do everything in their power to ensure that crypto is not bought with CBDC, maybe it will impact negatively on your social credit score or just regulated out of existence if it poses a real threat to CBDCs