They can be finicky about accuracy and are not as easy to improve accuracy with as a bolt action that can easily be "bedded" with epoxy.
I have one in 218 Bee which I honestly haven't done enough shooting with to know it's true accuracy potential. Groups in the 1 1/4 to 1 1/2" range have been normal with loads that I came up with trying to duplicate the old factory load using the Hornady hollow point 46 grain flat point.
The major Pro for me is the classic styling. I don't see how anyone could not appreciate a No 1. Especially if chambered for one of the older "classic" cartridges such as 7x57 or 300 H&H Magnum.