The invisible hand of the market has been handcuffed a bit here though. Though I imagine this will simply show up as higher cost rather than blanket inavailability.

The invisible hand of the market is already disabled by regulation, in this case trademark protection.

For example: if Nike is willing to destroy 100$ shoes, instead of selling them at 40$ discount, for brand protection, another shoemaker could try make identical shoes and sell them at discount. But the alternative shoemaker is not allowed to make identical shoes, this would infringe Nike trademark.

What do you mean? This is a case of a regulation distorting the markets ability to price and distribute goods.