Convert to profile
It should be possible to convert a documents colors via the same method as in Photoshop or InDesign via "Convert to profile" rather than "Document color mode". The current way makes it hard to correctly convert correctly and nearly impossible to convert an rgb color space to another rgb color space without using cmyk as intermediary step (huge color shifts and color quality loss).
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There is a way to covert a document to a profile needed.
You have to embed a profile into a document first, then change the working color space, then try to open the document (make sure though you have Profile Mismatch 'Ask When Opening' checked in Illustrator’s Color Settings). Illustrator will then ask you if you want to convert the colors for the document or leave them unchanged.
This is not a straight way, but it should work. However, just a command is welcome. -
Keegan Harris commented
This is sorely needed and for years now such a simple feature has been missing, so often I need to convert print files for digital use and there is no easy way to convert profiles in Illustrator, always such an unnecessary pain.