What MP3 players are you using?
Before smart phones, MP3 players were everywhere, lots of models for hundreds of dollars. Now, they seem to be extra cheap and cheaply made. Recently, I had a Sansa Clip+ 8GB that lasted two years - not bad for $40 and many, many hours of playtime. I bought another one, a 4GB to replace it, and it lasted nine months, survived a trip through both the washer and dryer and did pretty well I guess. Both of them now have bricked themselves. They simply will not respond to any button pressing, charging, or anything. My wife bought one on my recommendation and it was mostly a dud. The battery wouldn't last more than an hour or two. They seem to be very inconsistently manufactured.
I drive in traffic a lot and NEED an external button for skipping a song. I tend to put it on random across the whole collection - some stuff just isn't what I want to hear sometimes. The process for skipping a song with the Sansa is: Reach over and feel for the skip button, and press it, never taking my eyes off the road. With a smart phone, you have to push the power button. Swipe the screen. Locate the skip button on the screen and then press it. Lots of time with eyes off the road. It's dangerous.
But looking at Amazon, the Sansa seems to be the only thing out there. There are a couple others but really, there isn't much. I don't need it to play videos. I don't need it to connect to the internet. I just need a small screen to display what's playing, a USB connection to the computer, and maybe a SD card slot.
Also, Apple products (specifically having to use iTunes to manage my music) are completely out of the question.