an Anglo concertina which had a three-row keyboard and was thus chromatic

For melody, sure - but even on a three-row Anglo I bet there are plenty of chords that you can't get at all, and chord sequences that you can't realistically play (e.g. eight bars with four successive 'push' chords)

There are plenty of chords you can get on a 30 button Anglo. I think it is more useful to focus on what you can do rather than what you can't. As to your example, there's an air button which allows you to "take a breath"

The Anglo Concertina is a remarkably versatile instrument. I suggest you try and get hold of a copy of the 3 CD set "Anglo International" There is an amazing variety of styles of Anglo Playing.

Of course I'm biased; I attempt to play one and to accompany myself singing with one from time to time.