I kinda doubt it, but I guess you never know.
Apple and I guess Microsoft have such a huge head start on that.....I dont think it would even be worth Google to try.
PS- And in all honesty, aside from the people that just hate Apple..."because"....ipods are very nice.
You forgot SanDisk in your list.
SanDisk has tried and succeeded. They have 4 different MP3 players out right now. They just updated their Fuze to the Fuze + with a 16gb model and you can add a 32gb card to it (or whatever size of micro card you want).
SanDisk's MP3s are nice. I have a Fuze. I bought it because at first I didn't want to spend the money on an iPod (way overpriced for what they do not have), and found it to be superior with more features then the iPod Nano at the time (it competes with those) in my opinion. Then as my coworkers got iPods, I found out why I really like my SanDisk Fuze.
Yes iPods are pretty nice. The touch is nice (a coworker has that).
Although lately I've just been using my Droid 1. I put my favorite music on it or listen to Pandora. My music was easy to transfer to my Droid because of my SanDisk device, no special music player needed (like iTunes) to mess with. I do use my Fuze for relaxing or to help me go to sleep and as my "stereo" as I don't really have a decent one.
So yes, Google could do this and still make some money. Especially if they did a tough type device like the iTouch, I think those would sell more.
Although, like you said, I don't know if they really want to try. Partly because phones are becoming the All-in-One devices for people (that's what I do like about my Droid).