In theory, of course, a thermostat should hold the temp rating of the stat at any RPM. Auto Tstats/cooling systems do exactly this all the time. DD says that engines should not idle for long periods at less than 8 or 900RPM (can't remember which) because the temp will fall too low. So that indicates that at 1000+, the engine can generate enough heat for the temp to rise to whatever the Tstat can control.
So the Tstat, should be able to hold the eng temp in its appropriate range at any RPM from 1000 to WOT.
HOWEVER, the reality is that at least some of these marine DD cooling systems aren't that good. It's not a tstat limitation, it's a system limit. My 8V71TIs with 160 Tstats (oem spec) will hold around 165 at 1400RPM cruise and 185 at WOT IF the system is freshly cleaned. But that's not how it should work. If the cooling system was adequately efficient, the temps would not change to any great degree, the Tstat would just open/close as necessary to maintain the proper temp, like it does on your car.
Hotter stats would improve engine operation at the lower speeds we all seem to run now but could be a problem if you needed to run at high speed for any reason - WX, emergency, whatever. The PO had 180 stats in one engine (don't know why). At WOT it would run at 195; most folks think that's too hot for these engines. I discovered this when I was trying to figure out why one engine ran 10 degrees cooler than the other. When I was checking into this, DD had 160, 170, and 180 Tstats available for my 8V71Tis but per the engine serial number, 160s were originally speced so that's what I used.
I think often about going to 180's...