Frank,
In general I agree with your point(s) of view. However with some tunes you could play "dronish" with an Anglo and use the "series of hiccoughs" as a rhythmic support that sounds a bit hurdygurdy-like... (as Howard Jones states in his reply)
Listen to this Flamish Folktune that I recorded on a C/G Anglo concertina a few years ago. The melody (in C) is played on the C-row (right hand), whilst the "drone" (a G) is played with th left hand on the accidental row (when pulling) or on the C row (when pushing).
It is by the way a very good excercise for "decoupling" the left hand and right hand movements.
P.S. I just read the comment of Howard Jones after posting my original message, so I made an extra remark (between brackets and bold)...