Note that the URL bar does search autocomplete now (new in 55 maybe?).
Based on the diffs there, looks like the 55 feature can at least be turned off by setting the "browser.urlbar.suggest.searches" preference to false... (That preference doesn't affect the search bar.) Also looks like there's preferences UI for this (the "Show search suggestions in location bar results" checkbox).
I think there were talks about not presenting the search box for new profiles, too, but it looks like that hasn't happened yet.