While all needing all HQ equipment was true in the past. I don't think this will be true for Heavensword Three Star requirements. one would assume someone with all i180 gear will meet the minimum requirements (unless SE really hates their player base). And since i170 HQ gear with decent melds has higher stats... this means in theory you could have a few NQ pieces. They will be worth less, but still usable.

What they SHOULD do, is lower the overall materia requirements for maxing gear. Such that HQ gear is easily maxable and NQ gear is maxable but requires expensive materia (like they did for foragers/artisan gear). And this should be true for ALL PARTS including main and offhand gear. This would remove the severe punishment for NQing. But still cause a heavier cost to be incurred for NQing. Now as said above this may indeed be the true going forward, we'll just have to see.