Some users (like me) want something different from search than is available in most current browsers. The “omnibox” in those designs has lost essential capabilities.
Such users tend to gravitate to browsers with features that better address their needs.
I’ll continue describing the needs of one such user who I’ll call Steve.
Steve searches with a variety of tools (search engines etc.) and uses alternate tools when one doesn’t work well. When switching search tool he doesn’t want to retype search terms and wants a quick changeover. He keeps a record of some searches and sometimes edits these when creating new ones. In some cases he keeps a record of particular result sets, which he might analyse to determine which engines are worth using.
Where sensible he avoids search tools run by surveillance capitalists and their collaborators (or other objectionable entities), but is prepared to use these from time to time.
He finds the omnibox browsers unsuitable for his run of the mill work, instead using browsers that better support his requirements.
In that regard he finds the option in Firefox, to show a separate search box and provide a rapid way to switch search engine, particularly useful. Firefox and all browsers lack features that he needs. He is prepared (maybe with others) to code up the missing features to work with his own support systems.
I am aware that a forthcoming version of Brave will have a new API and new UI. How will it cater to a user like Steve?