You might hate me for this so I am ready for the grilling!!
When trading my old S3 8L the tyres needed replacing about 2 weeks before I traded the car into Audi.
I went for budget tyres because the dealer actually didn't give a toss about my car, the condition, or anything. It was mint!! The only thing they were interested in was the age, mileage and whether it had FSH which it did. When the salesperson looked around it he commented on the tyres saying "Looks like a lot of tread on those tyres, that's good, they're as good as new!" That's it!!
Personally I always had it on continentals or F1s and if selling privately I would've bought the same but the dealer was only interested in what he was selling to me.
The way I look at it is this... it is up to the dealer to get the car in a good condition to sell. Whether that's an MOT, a service, tax or something else, it's their responsibility. They put enough of a mark up on them when they sell as it is.
Anyway, I'm glad you complained and got a result.
In future, do what I do and negotiate on new tyres and all of the above when buying from dealers
Welcome, I'm sure you'll love your S3 once you get it