Unfortunately you can’t propagate properties for chord symbols in this way for boring technical reasons (they are system-attached, but appear in multiple places down the system, and each instance can have its own properties; the way that these instances are identified means that they are unique from one layout to another, so we will have to add some further special cases to try to achieve this, which we haven’t done).
In the forthcoming update you will have better tools to select chord symbols quickly, via a new “select more” command, and there will also be a command that you can bind to a key command that will hide chord symbols (and time signatures and playing techniques, at present the only items with dedicated ‘Hide’ properties).