Just for the record, you can absolutely change the default search engine in Safari and Firefox. I use kagi in both, so bangs are supported everywhere.
[1]: https://help.kagi.com/kagi/getting-started/setting-default.h...
You can change default search engine, but you cannot add extra search engines in Safari without building your own extension (and paying apple for it)
So does Firefox desktop...? Extensions aren't needed, just right click on a search field and add it. You can customise placeholders and keywords too
The resulting search shows up in the search UI, whether you have firefox configured for a seperate search bar or have their default of the address bar also being the search bar. This is the same as the extension method.
If your complaint is that they also show up in bookmarks, then ehh, whatever. Most people either don't use bookmarks or have a giant dumping pile. If you're one of the 1% that organizes them, just put all your search bookmarks in their own folder.
They aren't. Why do you claim things that aren't true?
Safari automatically detects search fields on websites and adds to the smart address bar. E.g. if I type "discmaster myst" Safari will suggest to search discmaster.textfiles.com for "myst". And that's something it automatically picked up. No plugins or configuration needed, users don't need to learn how HTTP queries work.