In order to block such sites, FR24, 360Radar, ADSBExchange, you would need to equip all of the very many "approved" receivers with the ability to process the new encoded squawks. Then you need to replace every transponder, in every aircraft. Look how hard it has been to get Mode-S and ADSB fitted everywhere.
The simple explanation of SSR is that it is broadcast, with the emphasis on broad.
How do you propose to stop some receivers picking it up, but not others? This is not Link16 or HaveQuick.
Once you have resolved the issue with FR24, how are you going to deal with the stuff that cost me just 85 GBP, to provide a live display in my house, and relies on nobody else? No internet, no feeds from NATS. Just a computer listening to the radio and translating SSR pulses to a visual image with a look and feel, very like a watchman console.