Leaving basement forms on permanently
Sounds like a hack-job approach to me.
That wall could be built from concrete blocks (aka CMUs or concrete masonry units), with bond-block rows and reinforcing steel, and grouted full, making it effectively solid, without abandoning forms in place - or rather, the forms would be the block wall.
Of course, poured concrete contractors and masons are not usually the same people, so this would not be a solution a concrete contractor would be liable to think of.
Alternatively, a form never intended to be removed and not made of wood that will rot - the insulated concrete form or ICF. Two sheets of styrofoam tied together.
But your pictures imply that this is a done deal.
If termites are a problem in your area, they may find that form tasty.