Sure, a shop can do what you describe even in German laws - every now and then.

However, if you do it systematically, if you offered that "special day" discount also yesterday and will offer it tomorrow then it's de facto the regular price, telling that it's valid only today is literally a lie, violates false advertising law (which goes into detail on how discounts can be advertised, so simply gaming it with definitions doesn't wowrk) and would get your store fined so hard for lying to customers.

Yes, misleading people to drive them over the edge works, that's the whole point. If it didn't work then we wouldn't care, but since it does work we as a society have chosen that we don't want that and merchants aren't going to be allowed to use such practices.