Not sure if I agree with your statement that "most tyres have a specific direction of rotation"? I certainly agree that they are not uncommon and, strangely enough? many of the really cheap and "nasty" offerings seem to be of this type. However I'm wondering if you're including tyres with asymmetric tread patterns? That is to say where the pattern is different on one side compared to the other - often a "finer" pattern on the outside shoulder compared to a much more "blocky" pattern on the inner. These types of tyre will be marked "inside and "outside on their sidewall and must be fitted with the outside marking facing out. However they are not directional so may be fitted anywhere on the vehicle. Many of the better tyres on offer today feature this type of tread and it does offer performance advantages, in fact I go out of my way to prioritize them when buying. Truly directional tyres are designed to move water from the middle of the tread to the outside and must be used the right way round - so, once mounted on the wheel can only be used on the side of the vehicle intended. They work much as tractor driving wheels do where the tread moves mud to the outside allowing better grip. Fitted the wrong way round they channel mud into the middle of the tread and greatly reduce grip.
It's also true that many of the highest performance tyres are directional and probably this type of design gives the manufacturer the scope to produce a less compromised and very high performance spec suitable for "super cars" and the like. Pandas tootle along very happily on good midrange spec tyres!