Suppose that a ham radio setup uses several antennas with a 50 ohm coaxial switch to operate some natively unbalanced antennas and some balanced ones through baluns at the feedpoint. An RF ground for all equipments in the chain going to a copper strip and then through a single point to the ground seems a good practice when operating unbalanced antennas, if I understand When is RF grounding necessary, and when is it not? well. But then, if the active antenna is balanced, should the RF ground be severed by a switch too? Basically, what happens if an RF ground is used with a balanced antenna (when a balun IS used)?
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This is a sketch of a common sort of balanced antenna — a simple dipole. Notice that it is symmetric, electrically as well as physically. There is no place to connect a ground; if you did, say, connect one side to earth, it would no longer be balanced (the impedance between that side of the line/antenna and earth would be greatly reduced while the other side would not, so it is unbalanced exactly by the definition of balance).
However, you also have a balun and you might ground the unbalanced side of the balun (or more precisely, the shield of the feed line as soon as it comes down in reach of a suitable grounding point). Theoretically, this makes no difference if the balun does its job perfectly and other things are ideal, but if not, this will reduce the unwanted common mode, and this grounding point is much better for this purpose than having additional grounding at the transceiver or other 'shack' equipment because it's right at the source.
From the perspective of the coax, a balanced and unbalanced antenna are identical provided they are properly installed. That means the dipole will need a balun, and the vertical will need radials (and still maybe a choke as well). In either case, at any instant at any point on the coax, the current on the shield is equal in magnitude but opposite in direction to the current on the center conductor. That is: all current is differential-mode; common-mode current is zero.
Electric charge is neither created nor destroyed, so if there's any current on the RF ground, there must be somewhere in the universe an opposite current to balance it. Because in the antenna setups under consideration the currents on the feedline are already balanced, and there's no "remainder" common-mode current, there is no such thing. So, there's no current on the RF ground.
As such, there's no reason to disconnect it. There's no reason for it to exist, either, aside from exceptional circumstances like a lightning strike or some kind of fault, like a powerline falling on the antenna. It's entirely irrelevant to operation of the antenna under normal circumstances.
Below is a NEC4.2 study of the effects of r-f current flow on the outer surface of the "grounded" outer conductor of a coaxial transmission line connected to an unbalanced antenna.
A true r-f ground does not exist at the top of an unburied conducting path whose base is connected to a true r-f ground (e.g., Earth). Any r-f current flowing on that conducting path produces e-m radiation for the same reasons it does when flowing on the antenna conductors, themselves.