I constantly accidentally hit the dictation button when editing URLs in the Safari address bar on my iPhone 7 (soon to be replaced, as iOS 16 drops iPhone 7 support), so I was looking for a way to remove the dictation button. For reasons that will become apparent later, the following screenshots are not from my iPhone 7 but rather from the iOS simulator in the Xcode developer tools.
Ah yes, the beloved "Not Now" option. How about… not ever?
I looked in Settings > General > Keyboards, but dictation was already disabled there.
Nonetheless, someone showed me a screen recording of the dictation button disappearing after disabling dictation. This got me to thinking: the screen recording was missing an essential step, i.e., enabling dictation. For the sake of science, I decided to try toggling dictation on and off, despite the unpleasant disclaimer that "Dictation sends information like your voice input, contacts, and location to Apple when necessary for processing your requests."
In retrospect, I feel the initial warning may have been misleading, because it implied that information wouldn't be sent to Apple unless you made a dictation request, which I wouldn't, but then when you turn off dictation it implies that information was already sent and needs to be removed: "The information Dictation uses to respond to your requests will be removed from Apple servers. If you want to use Dictation later, it will take some time to resend this information."
I'm not sure whether or not information is sent to Apple immediately. It's not entirely clear, and neither is the longwinded "About Dictation & Privacy" statement, unfortunately. It doesn't help that Siri and Dictation are commingled in the document. (By the way, why are the contrasting options "Enable" and "Turn Off" rather than "Enable" and "Disable" or "Turn On" and "Turn Off"?) Anyway, toggling dictation on and off did in fact remove the dictation button from Safari.
You can see this behavior both on your devices and in the Xcode iOS simulator. I mention the simulator so that you can simulate the situation where dictation had never been enabled, if you did already enable it at some point on your devices.
I consider it dickish behavior by Apple that they force you to enable dictation first in order to remove the unwanted dictation button, especially since enabling dictation seems like it might send your private information — such as contacts and location! — to Apple. So much for "Privacy is a fundamental human right."
Fortunately, a kind person gave me a tip on how to disable dictation without first enabling it: use Screen Time! Enabling Content & Privacy Restrictions in Screen Time and disabling Siri & Dictation will also make the dictation button disappear from the Safari address bar.
Of course, then you won't be able to use Siri at all, if you care about that. I've never personally used Siri even once, not even as a joke.