Strength is fairly unique among Abilities in that it serves actual purposes other than just boosting stats and skills. Operating under the premise that lifting rank and miscellaneous Strength functions work out to about 1 PP/rank in value, it's also actually technically advantageous point-wise (1 PP/rank for Damage, 1 PP/rank for lifting and misc stuff, 0.5 PP/rank for Athletics). That said, the same premise does apply; if you want lifting rank, and you want Strength-based Damage, it's perfectly solid and you even get some Athletics for free. But if you're using Strength, you want to either use only attacks that are Strength-based, or to make sure you use things like Reduced Strength Damage to offset it for your non-Strength-based attacks (or your GM can just make it easy on everyone and say the Strength bonus applies to any type of attack, though only one at a time, regardless of if it technically has the fluff of being propelled by muscles). Otherwise you're just paying twice for your damage.