Aww man, that just took me down memory lane. Minidisc was, imo, the peak of portable music players. Huge capacity, swappable/tradeable media, excellent sound quality, the little inline screen you mentioned. A quick Amazon search shows they're still available.
Three button inline controls usually gets you pause, volume up and volume down. This is essentially 5 buttons: pause, forward, back, volume +, volume -. Sure there are probably wired headphones that have the same control capability, but I've encountered them rarely if ever.
And I've gone through at least three 3-button headphones that have only worked with volume and pause. I suppose one could use the volume for track control with some sort of special logic, like a longer button hold. But I've never encountered that. The Bluetooth headphones I have actually has another set of capabilities which is to not only skip or go back in terms of tracks but also fast forward and rewind within a track - very useful for podcasts.
The standard iPhone headphones since the 1g support all those. Click to pause, double click for forward, triple click for back. Long press on the second or third click for rewind/fast forward.
5 logical buttons with 3 physical buttons was something of a standard since time immemorial - the volume+/- buttons doubled up as next/previous when you held them.
There's absolutely no reason why wired headphones can't do that, you can buy ones with three-button inline controls. Ye olde Walkman could do it.