Right now, there are only two kinds of weapons that can go S-Upgrades viably:
Magic Weapons
Possibly Taunes for the purposes of HM grinding.
All other weapons benefit more from R-type upgrades.
In addition, S6 for magic weapons is considerably weaker than R6 is for melee weapons. R6 increases average damage by 18.6% (62% * 0.3).
S6 increases average damage by a flat amount which translates to considerably less of an average damage boost that suffers from the law of diminishing returns (yet R6 is even worse because while R6 does pass S6 in average damage above a certain MATK breakpoint, that breakpoint is rather difficult to reach, and sacrifices consistency for burst, and magic already has burst).
Possible solutions:
Nerf R-type critical damage
Change S-type damage into a %boost (roughly along the same lines of pre-Druid magic S upgrades)
Make 30% critical harder to get without sacrificing max damage
Increase MATK and base attack gains from S type
Add additional effects to the stone types to make the choices meaningful