I'd like to add to the case for singing to the Anglo. I've been accompanying song with a C/G Anglo for 25 years, and though I've gotten to the point of being able to do a lot of what I want, I'm still discovering new capabilities all the time.
I accompany songs in these keys on my Anglo: C, G, D, F, Dm, Am, and Cm. I'm working on Bb and A. I find the trick is adapting the accompaniment to the key; in most of the keys I can play chords on the left hand and melody on the right. But for some of the more esoteric keys I use a melodic or harmonic line instead of chords.
The Anglo is pretty versatile, and once I learned to use all 33 buttons on my box I was able to produce a broad range of chords and notes (in fact, I use many of the same notes that Beethoven did :0) sorry, got carried away there). I can play in the "English style" -- chords on the left, melody on the right and the "Irish style" -- straight, smooth, rapid melody. So I have a choice of the bouncy in-out in-out feel of a diatonic instrument as well as the long legato passages (within reason, of course) one can achieve on the English concertina.