Max pressure allows the tire to support it's max rated weight. A 16" Sailun S637 probably supports 3,750 lbs if inflated to 110 psi (cold).
On a 2 axle coach, that would give you 15,000 lbs of capacity on the 4 tires.
A coach with 16,000 lbs GVWR is probably carrying around 3,200 on the pin, and 12,800 on the tires. So with a fully loaded coach, you would have 2,200 lbs of margin on your tires - assuming even distribution of weight.
But weight is rarely distributed evenly. So you could have one tire carrying 3,200 lbs. Another carrying 2,900 lbs., another carrying 3,500 lbs. All less than the rating of 3,750 lbs.
I'm a believer in having a good safety margin on loading. If you did have one tire carrying 3,500 lbs, leaving only 250 lbs of margin relative to the tire's max load of 3,750, I'd suggest trying to rearrange stuff to shift weight. Or move to 17.5" tires that will carry more weight.