It doesn't matter how hard the ACs work. I mean they're either on or off unless you have variable speed fans and compressors which is what I'd suggest. Still, the AC is most efficient when it's running and the longer it runs the better so the variable speeds running at low capacity for long intervals is the most efficient.
It makes no sense to me that it wouldn't be cheaper to do batts vs foam so make the builder spend his money and install the foam which is obviously what he likes. Sounds like he's done the math for AC size based on foam and it won't make you any savings to skip it so let him do what he's planning.