I have seen gold metal level plans high deductible health plans that qualify for HSA. I do not know about platinum, but the difference in gold and platinum is gold covers 80% of expected expenses and platinum covers 90%.
My gold level high deductible health plan has a ~$3k deductible I think (for family coverage).
I imagine even a platinum plan can be high deductible if the deductible is set to equal the out of pocket maximum.
Either way, the numbers will not be too different for gold and platinum plans.
People on traditional plans can have FSAs but those typically don't let you really accrue from year to year.