Should I set deck post footings deeply or use concrete footings?
It works for pole barns, it will work for your deck. However, be careful of the quality and/or treatment of your PT lumber - I've seen pressure treated lumber rot off in the ground despite being pressure treated. I think the thicker sections (such as 6x6) are rather difficult to get throughly treated all the way through. I've seen some pole barns use 3 2x6 laminated (though that was ALSO a trick to be able to have PT in the ground and non-PT above the ground, by having a staggered splice in the layers after it was above ground.) Presumably there are more carefully done ones that are "post or piling" grade and less well done ones that are "landscape timber" but in many cases there's just one type in stock, take it or leave it - so you might want to look into it more and figure out when you should leave it and shop elsewhere, or special-order something different.