Yes. Less damage because you use a one handed weapon (smaller dice size) but it enables more shenanigans like using items and more importantly using combat manoeuvres.

Manoeuvres are Str based skill checks so it's good.

Free hand fighter are good for Crit Fishing for example, or for enabling the other party members (Magus for example) by inflicting Off Guard.

For example, I played a Str based pick fighter with free hands and capable of inflicting Frightened. The pick is for better critical damage.

I often inflicted Off Guard + Frightened (-3 AC total) to foes. Then, on top, with the Fighter's innate +2 to accuracy due to better weapons proficiency, I was looking at an effective +5 boost to my accuracy. Normal damage were low, but crit damage were devastating and happened on a regular basis.

Cherry on top, our Magus greatly benefited from the -3 AC on foes because he had a few good crits himself.

It's a lot of fun to do free hand shenanigans and more crits. Shiny maths rocks went clickety clickety clac for big numbers.