VLC - does MORE than you think

bin/cue files are CD images, similar to .iso files but often (not always) containing multiple tracks rather than just one.

You can read the .cue file with Notepad - are you sure the tracks are identified as AUDIO? If they are MODE1/2048 or 2352, they're data tracks.

You could use ISObuster to open the image and save the tracks as separate .wav files (if they are indeed audio).

Correct. Imgburn will by default want to create an ISO as the file format for data discs and bin/cue for audio. So if I make a backup copy of one of my audio CDs imgburn will produce the continuous binary copy .bin and a .cue file describing the track info.

In principle VLC should be able to play bin/cue file combination directly. How do get it to do it (without mounting a virtual CD)?

Yes that's what I thought but it doesn't work for me. I have the latest version of VLC. Does it work for you?