I wouldn’t have believed it if I hadn’t experienced this myself, but I had new tires put on a car several years ago.
What do you suppose the tire shop thought when I immediately returned to tell them that my car had a bad “pull” that wasn’t present when I went in for tires? Of course they thought I was nuts or trying to blame them for a problem I already had.
I got them to ride with me and then swap tires from side to side. On the next drive the car pulled the opposite direction.
After they replaced the defective new tire(s) the car didn’t pull.
Older tires can certainly develop problems with belts/structure that can cause extremely unusual wear (I’ve owned some) and it makes sense that they could cause a car to pull quite noticeably.
Road test, Road test, Always.