No one wants that, most websites become broken by taking pro-privacy measures. It's about not consenting to tracking. Right now the majority of users are implicitly giving consent to tracking.
It seems like a harmless thing to be tracked, but once the likes of haveibeenpwned.com came out and the databases that fuel it, and services that provide search utility to those databases, it should become clear that being tracked across every single website on the internet is probably not what you want.
Scenario: You apply for a job, they look up your totally-clean email address, see the email linked to an ip address on some database from a leaky website you applied for a job on, the ip address is linked to a service where you used a certain password which you used on 6 other services, one of which had a database leak of your system fonts, now you can see all the accounts to services to which your system fonts were identically matched. Oh look, you were 13 years old when you joined stack overflow on an abandoned account and you posted some humorous, incorrect solutions that were down-voted to oblivion. But that's ok, they invite you to the job interview and they make a funny remark about your stack overflow answers and then offer you a job. Do you want to work there now that you know they completely invaded your privacy ?
And yes, performing such searches is trivial.