If this CBDC can process payments within a few seconds or minutes (some Blockchains are able to) that's also a huge win for merchants as that means they actually have the funds they need to fulfill orders rather than relying on credit (which also costs $) and having to wait days for all customer's funds to be deposited.
Rapid settling times help cut down on fraud - which itself is very costly to businesses (the cost of which is carried by the consumer).
So by switching to a quickly settling CBDC, businesses can save time and money - savings that can be passed to consumers. Now, whether they ever do that is another question.
Control. If you're of the mindset that there is an upper-class and a lower-class, you're incentivized to create a form of money that makes both permanent. This prevents competition, generational wealth transfer, and guarantees infinite, cheap obedient labor.
The movie Elysium is a great caricature of where this will lead.