I see no advantage to 4" concrete cores. The cost difference in concrete is negligible and trying to run rebar and consolidate in a 4" space is not easy. From everything I read, 4" is the absolute bare minimum thickness of structural concrete.
If concrete costs $82 a yard for a 3,500 psi mix, delivered to the site. Let's run the numbers for 2,500 square feet of wall space:
6" core = 46 yards of concrete = $3,800 of concrete
4" core = 36 yards of concrete = $2,950 of concrete
You saved $850 in concrete. That is basically insignificant when speaking in construction terms. The contractor will probably still charge the homeowner $3,800 for the concrete and pass the savings onto himself.
