Nothing wrong with 200*. Most fwd cars with electric fans were designed to have fan come on around 220*, off at 195.
I just put a thermostat in a Chevy Cruze last weekend for a buddy's kid, and couldn't believe it but all listings I saw said that stat doesn't open til 221*.
My 12, 1/2 ton with 4.7 has a 195* stat and it runs between 200 and 203* on a warm day.
There is such a thing as being too cool as well.
I wouldn't worry about a 200* running temp although you said you have a 160 stat? That's the only surprising part is that you're that much above t stat rating.
I'd run at least a 180 in there if bet that engine runs at the same temp it does now.