...and they do - on rotational tyres; not asymmetric tyres.
You can if you turn them on the wheel.
How do you work that out if they have inside and outside printed on them?
That does not address the matter of the tread rotating in the other direction.
Therefore rotating in the other direction is not desirable.
I think this article explains it best and seems to agree with what I am thinking:
"Directional Tread pattern
Directional tyres will usually exhibit an arrowhead-like tread pattern which provides a very striking appearance. But there is more to directional tyres than just appealing looks. There is an obvious compromise when designing a tyre that works just as well rotating in either direction. Asymmetric tyres do just that and in some respects this limits their performance. Directional tyres are designed to rotate in a single direction and as a result they provide excellent wet weather performance and good directional stability. Because directional tyres offer excellent traction, they also perform well on snow covered roads. That’s why many winter tyres have directional tread patterns.
Whereas asymmetrical tyres can be fitted on either side of the vehicle, directional tyres can only be rotated vertically (i.e. from front to back) otherwise the tread pattern will rotate in the wrong direction when mounted on a wheel on the other side of the car. An arrow printed on the tyre sidewall will show the required direction of travel which will also match the arrowhead shaped tread pattern."
Sorry, but isn't that exactly what I just said?