I have a closed radiant heat system, meaning a boiler with a pump, radiators and piping. After the intake valve, there is a pressure reducer and a backflow stopper (both bell shaped). Yesterday, when I was reenabling the system after I had dismounted some radiators for painting, I had forgotten to tighten the elbow couplings on one radiator so when I was filling the system, I had a small flood. Which got me thinking, if there ever was a leak while I am away, the open intake valve would cause continued flooding but if the system is full, as it is a closed system, the spillage would be limited. So there is an advantage to having the valve shut. But are there any reasons to keep it on?
That would depend on how smart your boiler controls are. If they shut down on low pressure, there's no real reason to leave the valve open. If not, you have flooding on one hand, burning out the boiler on the other...neither is good. Smart boiler controls and a closed valve would appear to be the best available option.