> While almost everybody including me shares this perference maybe it should be something that browsers could do? After all why put the burden on countless various websites if you can implement it in a single piece of software?

If I recall correctly, Apple tried to do that and it (rightly) elicited howls of outrage. What you're asking for is for people's own computers to spy on them on behalf of the authorities. It's like having people install CCTV cameras their own homes so the police can make sure they're not doing anything illegal. It's literally Big Brother stuff. Maybe it would only be used for sympathetic purposes at first, but once the infrastructure is built, it would be a tempting thing for the authorities to abuse (or just use for goals that are not universally accepted, like banning all pornography).