I have always left the propane on , except when refueling.
I have never had a proplem, nor do I expect to.
One camper the flame on the fridge would blow out and the propane would shut off, but redesigning the sheild helped that.
We have towed from Elk River, Mn to Washington state nonstop and the food would be junk if we shut the propane off.
There's lots of new stories where somebody has gotten hurt or killed becaue "I've never had a problem with xxxxx"
Recent example. A couple of ladies were warned that walking on Oregon beach this past week might not be safe. They've walked on that beach millions of times and chose to ignore the warning because they'd never had problem. They don't have to worry about it anymore, they were washed out to sea.
Seat belts is another one those. You put a seat belt on when you get in vehicle not because you expect it to be needed but because it might be needed. I grew up without seat belts and survived, some of my high school friends weren't so lucky.
The point is that the chances that you won't have a problem are pretty good, but the results of a problem could be quite large. Is it worth the risk? When somebody is going down the road with porpane on are they risking other people's lives?
There's lots of things we wouldn't do because of the slight possibility of something bad happening. It's a small thing to turn off the propane while traveling and reduce the one more risk.