what's the whole point of the query/Ctrl-E in Chrome

In case you enter something that looks like a domain name, but isn't (in the context you're using it), like e.g. Microsoft .NET related technologies (Visual Studio .NET, VB.NET, etc.), and you want to prevent the browser from helpfully interpreting it as an URL.

Also, the search results for a domain sometimes can be kind of interesting, and this is one way to get them, instead of viewing the site (e.g. Which Google services are on the top ranks when searching for google.com?). Googling for a web shop domain can also find reviews for merchants you might be interested in buying from. There are quite a few scenarios where you want to learn about a web site, and not go to the site.

Daniel Beck's answer is correct in addressing Google's intent.

I think it's also worth noting that if you use Ctrl+e from inside Chrome Dev Tools' Timeline tool it will begin a recording. However, if you then click anywhere on the target page you're testing, it will shift Chrome's focus away from the Timeline tool, rendering a second Ctrl+e incapable of ending the recording, as Chrome will instead open a query. This seems to be an oversight, rendering Ctrl+e unusable for discrete test purposes.