It’s specifically advised for use on the nano texture displays, where the wrong material could rub away the special surface etching they use to get the glare resistance.

They list it as compatible with everything, because, well why not.

As someone who actually has the nano texture display and has actually used Apple’s cloth and regular microfibers:

the main difference seems to be that the Apple cloth will clean finger grease out of the nano texture. With a normal microfiber you have to spend five times as long, spray windex, and rub really hard.

I have the nano texture on an iPad, and I wasn’t too concerned about scratches, but after years of using both I still don’t have any

IKEA recently changed their microfibers to be more like the special Apple one, and they work now too

As someone who actually has the nano texture display and has actually used Apple’s cloth and regular microfibers:

the main difference seems to be that the Apple cloth will clean finger grease out of the nano texture. With a normal microfiber you have to spend five times as long, spray windex, and rub really hard.

So using a wrong polishing cloth will damage that special surface, but not the inside of my pocket?

Are you able to fit an open MacBook Pro with nano texture finish into your pocket? If yes, you might have different problems (or benefits).

The special etchings aren't used on iPhones

It’s an option that costs extra and is only available on some MacBooks and Studio Displays, not iPhones and the like.

It's a special surface finish for living room TVs. Not intended for touchscreens.

there are no nano-texture display devices that fit in a reasonably sized pocket

This is why AAPL is a 4.62 trillion dollar company.

It's because they know there is a segment of fanboys that will buy it.

Apple devices are fashion accessories, like sunglasses and watches, which all come with polishing cloths.

Marging and fingerpointing in case the customer damaged the screen with some "third-party" cleaning cloth.