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UK households could face VPN 'ban' after use skyrockets following Online Safety Bill
(www.birminghammail.co.uk)
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No, there are very good technical reasons why this approach can't work.
There is no deep packet inspection on properly encrypted TLS connections. I know TLS termination and interception and recertifying with custom certificates is a thing, but even if it were feasible to implement this on millions of client computers that you don't own, it is an absolutely god awful idea for a million reasons and much worse for privacy and security than the age-gate problem you're trying to work around.