That sounds simple when you say it but persuading merchants adding new exotic payment methods is a tall order. Do they need to buy a new device for processing DAI payments? That is extra expense they don't want. It would depend heavily on how the integration is done.
Do you need to train their stuff how to accept new payment method? Also now they are holding money in multiple places (bank account for normal payments, some wallet for DAI) so this introduces another overhead for them to handle.
How many people will pay with DAI? Will it be more than 0.01% of customers? Because there are almost no people who own DAI (nobody outside of crypto bubble), so you have problem on customer side. And why would merchant go through the trouble of supporting new payment method when it will be only used by a minuscule number of people (there are merchants that tried supporting Bitcoin payments and it turned out they had like 1-2 people paying in BTC in months so they don't bother anymore.)
I don't see it happening personally unless it can be done in a completely seamless way (for both merchants and customers) and I don't think that's the case. Existing payment methods are too entrenched and very convenient. People actually like using credit cards / Apple Pay etc. It's easy and user friendly.
The few places that accepted Bitcoin payments back in the day when it was trendy, it looked really weird and inefficient, people scanning QR codes, having to use special mobile apps to handle the payment instead of POS merchant already has and knows how to use. Seemed kind of pointless.