Yeah, checking wheel alignment is a fairly quick job & adjusting the toe on modern vehicles are fairly easy.
It can be done it 10-15 minutes on front wheel alignment.
Most tyre places do the second check for free I reckon, 'cos they would like you to come back.

If it has fixed the problem, that means you gota free wheel alignment.

If it hasn't then it must be the tyre.
I don't think factories check each tyre for manufacturing faults. May be they do occasional one or two out of the production line.
On some occasions, wheel alignment issues or vehicle dragging to the side on straight flat roads can be caused by structural damage to wheel alignment by accidents(collisions or hitting chassis parts on hard rocks, etc).
In same cases, after crash repair the pulling to the side on flat road are hard to correct, even though wheel alignment readings on the display(toe, camber, etc) can be corrected to the accepted ranges.
Keep an eye on the tyre wear pattern. That's more important.
Ages ago, I drove a Ford that had tyre wear issues that couldn't be fixed without spending a fortune.