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).
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.