White foam when cooking chickpeas, what to do with it?
The white foam is a 'scum' that is formed as protein is released from the chickpeas. Yes, that is the term that is used. Scum.

This can be skimmed for aesthetic reasons - it sticks to the pot, or overboils, etc...

You are absolutely right, though, that if the chickpeas are rinsed after, then this is washed away.

If you are draining and pureeing, it will just incorporate into the dish.

Totally an aesthetic choice in my experience.

Similar to meat protein scum, referenced (What is this in the beef stew?)