One stat to rule them all, or what if we merged Dex and Str?

[diplomancer]

Say I want to play a nimble waif. I use leather armor, a Rapier, get proficiency in Acrobatics, Stealth and Sleight of Hand (but not Athletics), and go around trying to do Acrobatic stunts. I choose feats that enhance that archetype. I play a Rogue Swashbuckler. And every time I make a Physique(Strength) check I reinvent the Strength attribute by applying a ad-hoc penalty to my Physique check to fix it being too high for the characterization of my nimble waif character?

How is it that my character is NOT a nimble waif using the Physique attribute? Because I had to reinvent the Strength attribute to fix the thematics. Physique gets 0 credit for characters that result in me reinventing Str/Dex.

No. You just roll the check as is, no penalty necessary (as that would indeed defeat the whole purpose), and try to come up with a description that fits what you picture for your character. Houdini was not particularly strong, but he could still escape bonds quite well (to use an example of a mechanic that's usually done with Str).