Seriously not everyone has a second monitor and not everyone even has room for one, adding this wouldn't be that difficult or time consuming.
Then buy one. Or get one gifted. I have two of them in storage.
Seriously, why should people's shortcomings in hardware be FD's or other player's problem?
Multi-Monitor setups have been standard since more than a decade now.
It's already a big issue that game developers are not skilled enough to make use of them. There are a few exceptions (DCS, Supreme Commander..) and the folks over at Nintendo with the Wii U Tablet Controller are doing fine as well, laughing over the inability of PC devs.
Except for UI elements, there's no need to devote time - one can whip up a player's core code during coffee break with public domain code and/or calls to dlls which ship with Windows by default.
We see how FD struggles with such trivial things like integrating ship names - which is an alter table statement, some SQL code and some UI code. And we are still waiting for it since over a year.
If you put such stuff in like a music player, it will take until 2020 and consume considerable resources - for a thing that people already have.
Instead, make it worthwhile then and integrate a whole API, so the community can develop.