I think this is an under appreciated point—and impressively clever/sneaky on Apple's part.
A user who taps the Safari icon is expecting to get Safari. If they are subsequently presented with a screen that says "would you like to use a different browser instead," the user is likely to respond "uh, no, please just give me Safari like I asked."
By contrast, if the browser choice was presented as part of the initial iOS setup flow (where you are asked to choose between light and dark mode, enable Siri, and so on), users would likely be much more amenable to selecting a different browser.