I really do not like to use "starred" targets in any way:
x, y, * = iterable
This one won't work, because it looks like in-place multiplication (__imul__) which clashes with the above for a single name as assignment target:
x *= 2 # "x = x * 2"
x, y, *...
Because any "starred" target implies consuming or collecting, and contradicts with the proposed behavior.
Consuming does not contradict with your proposal, but maybe you mean *fully consuming*. I think you are proposing partial or incremental consumption of the rhs.