On iOS, there is an app called xSearch that integrates into Safari and sneakily hacks around the limited search engine options by watching your browsing history for queries to the search engine you've selected in Safari, then immediately rewriting the URL and navigating to the search engine you actually want.
Obviously this has security implications, but I don't ordinarily search for anything sketchy on my iPhone so I'm personally not too worried about it.
Using third-party browsers on iOS isn’t nearly as annoying as it was a few years ago. I had been driven to switch back to Safari a few years ago after trying to make a go of it. But last year I switched back to a third-party default browser and have been happy.
Third-party keyboards, still not usable but browsers are basically ok.
Obviously this has security implications, but I don't ordinarily search for anything sketchy on my iPhone so I'm personally not too worried about it.