Telco COs suffer about 100 surges with each storm due to copper wires all over town. How often is your town without phone service for four days after each storm while they replace that $multi-million computer? Never. You must do what they do.
Your concern is for a direct strike that hunts for earth destructively via interior appliances. That ethernet wire is exposed - not protected by something that is lightning conductive - wood. So use another proven technique. A lightning rod (and this is what actually does the protection) connected to an earth ground means an ethernet wire below is unlikely to be a victim of a lightning strike. Any lightning that seeks earth will use the lightning rod and not your exposed ethernet wire.
Protection from lightning is routine. But that means understanding a fundamental question. Where do hundreds of thousands of joules harmlessly dissipate? A lightning strike far down the street means lightning is incoming to every household appliance. Your TV cable has a hardwire that connects that cable low impedance (ie 'less than 10 feet') to single point earth ground. That means a surge connects to earth BEFORE entering the building. That means hundreds of thousands of joules dissipate harmlessly outside in earth.
Telephone and AC electric cannot connect directly to earth. So we (and that telco CO) do what has been proven by over 100 years of science and experience. Connect every wire inside every incoming cable to earth directly or via a 'whole house' protector. Again, protector does not do protection. Earth gruond absorbs that energy. Protector is only doing what that TV cable's direct hardwire connection does better.
That is the point. How does a surge current get to earth. Either harmlessly outside. Or it goes hunting for earth destructively via appliances.
Ethernet shield is for noise. Would be grounded at one end to a chassis of that appliance. Should lightning strike the shield, then lightning is connected destructively to earth via that appliance.
For a shield to provide tiny surge protection protection, it must connect a completely different ground - earth ground. An ethernet shield first must drop down to the single point earth ground to make a low impedance (ie 'less than 10 foot') connection to earth BEFORE entering the building. Surge protection is always about how that surge current connects to earth.
What would an ethernet protector do? Is is connected low impedance (hardwire with no sharp wire bends) to single point earth ground? If not, then it only protects from other surges already made irrelevant by protection inside all ethernet interfaces.
Appreciate the many electrically different grounds. Chassis ground is completly different from a wall receptacle safety ground; is completely different from earth ground. All may be interconnectded and are still electrically different grounds. Term 'low impedance' makes that obvious.