Opera (pre-Chromium) had this feature to begin with, then Firefox (using bookmarks to store the keywords instead). Vivaldi browser retains the Opera style custom search UI and whenever I find myself searching a site enough I just create a nickname for it (eg: to archive the URL directly to archive.org/is, search caniuse.com, among dozens of others).
Too true. I've wondered for a while what the keyword field in a bookmark was for.
I also found out just the other day that I can add search engines to Firefox[1] if the site supports the OpenSearch API[2]. I didn't know they could be added this way, nor did I know about OpenSearch, if I hadn't have searched for an easier way to search a site I frequent then I would never have known.
[1] https://support.mozilla.org/en-US/kb/add-or-remove-search-en...
It's incredibly well hidden though, and the UX is horrific, which I'm convinced must be deliberate.
For anyone else on Firefox, there's no need to go through a search engine or install anything. Just follow the instructions in that link. It'll change your life.
This feature has been implemented since I started using firefox, circa 2004.
[1]: https://support.mozilla.org/en-US/kb/how-search-from-address...