Are you also okay with it giving it to every party the search provider gives it to? Business partners (?), employees snooping, government agencies (with or without lawful process), hackers who've compromised the provider's business?
Are the people who's sites you're using also okay with you passing URLs on their sites to your search provider? Do you ever accidentally paste confidential text in the wrong field?
Because there is no way to tell if the data is being logged (or, importantly, to prove that it isn't) it is prudent to assume it is, with an infinite retention— will your opinions about sharing todays data change if the search provider's behavior changes tomorrow? if some relevant government changes policy tomorrow? Does the fact that you can't ever take it back concern you?
These are some of the things I think of about it— and are why I wouldn't intentionally use such a feature regardless of how positive I feel about my search provider. And because of these thoughts— especially that I can't really make any binding commitment to future policy, or really guarantee that my policy is being followed (e.g. intelligence agency plants on staff) if I were a search provider I would not run such a service, unless I could figure out a way to build it such that I _couldn't_ turn evil, knowingly or unknowingly today or tomorrow.
Lets not pretend that every keystroke you type into the Omnibar being sent to Google is the same as using Fastmail. They're extremely different from a privacy perspective.
Let's not pretend that Chrome forces you to send every keystroke to Google. It's a feature controlled by a check box that most people find convenient.
It's exactly like using Fastmail. It's a convenience over self-hosted mail that sends all my email to Fastmail. Just like Omnibox, you have a choice to use it, and just like Omnibox, it sends a lot of personal information to a third party.
When I use gmail for mailing lists it doesn't result in Google getting my self hosted personal mail or my work mail. It's not really analogous at all. And even if it were— a different privacy leak doesn't make other ones irrelevant.
The point is it isn't a privacy leak at all, and we were never talking about mailing lists. We're specifically talking about whether Omnibox is a feature that should never be implemented by anybody, as you originally claimed, because it gives away too much information. By that same argument, hosted email shouldn't be implemented by anybody because it gives away even more information.
The reason people don't complain about hosted email is the same reason it's ridiculous to complain about Omnibox. Even though it gives information to the service provider, the service provider provides value on top of that information that makes a vast majority of people prefer it to the alternative, which people also have an option to use (by unchecking a check box or by running their own mail server).
Are the people who's sites you're using also okay with you passing URLs on their sites to your search provider? Do you ever accidentally paste confidential text in the wrong field?
Because there is no way to tell if the data is being logged (or, importantly, to prove that it isn't) it is prudent to assume it is, with an infinite retention— will your opinions about sharing todays data change if the search provider's behavior changes tomorrow? if some relevant government changes policy tomorrow? Does the fact that you can't ever take it back concern you?
These are some of the things I think of about it— and are why I wouldn't intentionally use such a feature regardless of how positive I feel about my search provider. And because of these thoughts— especially that I can't really make any binding commitment to future policy, or really guarantee that my policy is being followed (e.g. intelligence agency plants on staff) if I were a search provider I would not run such a service, unless I could figure out a way to build it such that I _couldn't_ turn evil, knowingly or unknowingly today or tomorrow.