All running them cold does is wear them out quicker.
put them back in, and check to see if the poppit valve is all there too.

Thermostats keep and engine running at a designed to operate temperature. Too hot is trouble, but too cold can also be. From what I understand, the high reving merc 260, 280 and drags do not have thermostats. Those engines need to be run in “warmer” water.
For everything else, put them back in!
Removed thermostes are not a solution for low water pressure/volumn because of too high of lower intakes or impellers that need changing.

I would put them back in, it will help keep the block temp more consistent. If you don't have a water pressure gauge it would be a good idea.

I just found out the thermostats have been removed from the Mercury 150HP V6 that is on the Viking I recently purchased. I live in Louisiana so it does get pretty hot and the water temperature will be warm also. I was told they were removed to be sure there was a;ways enough water flowing to keep the engine cool. I guess it makes sense in a way since the water is a flow through not like in a car where it is recirculated. My question is do iI need the stats or can I just leave them out. The tell tale flows water almost as soon as it is crank which on a mercury I believe the tell tale was after the stats so wouldn't flow until they opened.