To my understanding, an effective Hard Hitting player is going to need to have high tackling, speed, strength and agility.

However, the Hard Hitting Strong Safety archetype's 4 majors are Vision, Strength, Speed and Tackling while the Jack of All Trades SS are Agility, Tackling, Speed and Strength.

Wouldnt it make more sense to use the JOAT archetype for a hard hitter as opposed to the HH archetype, considering big hit is less useful than monster hit, so the favored SA isnt as important?

If you're building a SS that's going to play any sort of coverage, speed and vision have got to be your top two attributes, imo. The hard hitter archetype gives you the ability to make a good zone SS for knocked loose opportunities.