That’s old style thinking. If that type of matching isn’t already automated and running, it will be soon. They’ll click a button and find you everywhere if you’ve left enough breadcrumbs, so there won’t be any lengths to go to. And as someone who has gone through the cybersec exercises of hardening browsers against fingerprinting, knows what VPN can do and more importantly what it CAN’T do, etc, I can say there are precious few people in the world going to the lengths required to stay truly anonymous. It basically has to become your top priority and constant focus if you want to be successful.
For the government, it’s always worth it as long as the funding is flowing. After all, it’s not like they are footing the bill. You and I are paying for them to spy on us.