It's never that easy because you have bypassed some very basic requirements in your question. For a start you need to be able to "link" the recorded vocal audio to the backing track - you need to be able to play the backing track and hear what your good lady has sung without suffering timing differences that can make it sound like a mess.
At the very minimum you need a two track playback device - track A is the backing and track B is the wife.
But why would a designer of such a simple product stop at this point? They'd make it capable of shed-loads of tracks - they compete in the market and if someone brings out a product capable of three tracks they are dead in the water.
You actually need more than two tracks anyway. Consider this - the good lady wife records a vocal track but verse 2 could be better - what to do? Record the whole thing again or have a third track that would be used for the parts in the 2nd track that needed redoing?
The 2nd track could have facilities for muting the vocal where track 3 takes over - you play it back and it sounds seemless because both vocal tracks together give you the result you want.
Already this is more complicated than your original question and justifiably so. How is she going to apply subtle harmonies in places without having at least 8 tracks? Original backing is 1, then main vocal (plus muted area) is 2 then 3 is fixes for verse 2 etc., then 4 and 5 might be left and right vocal harmonies with 6 and 7 making it a 3-part. OK maybe 8 isn't needed!
What about eqing her voice - I don't know anyone who sounds good straight out of the mic without eq and a little bit of reverb. You need to be able tro trial eq and reverb (plus any other fx) so things are a bit more complex and you are heading towards a DAW.
Get used to it - you think you know what you want but you don't.