I don't know about the pool builder you are talking to, but when I built my pool primary factors in cost were the perimeter measurement, area and depth. Some used volume instead of area, but all used perimeter as one of the factors. That, of course means that for a given area, a long skinny rectangle would be the most expensive shape, and a circle the cheapest. Free form is cheaper than rectangle, since removing corners reduces perimeter. I know I paid extra. By planning two rectangles merging corner to corner we ended up with a lot of perimeter.
Same here. The cost from our PB was based on linear feet of perimeter. There was hardly any difference between a rectangle and similar size free form shape. It's all in the perimeter length.
I also love our free form shape. I grew up with a rectangle pool and there's nothing wrong with them, I just love the look of the free form and how it changes up the look from your average rectangle. We've had so many comments on the shape of our pool, everyone that comes over and first sees it says they love the shape. Gives our back yard a resort feel.