Having the menu exist at all is already well onto the slippery slope - once upon a time the screenshots went directly into the photo library, without any interstitial at all...
And at the time, everyone was perfectly fine with opening the photo library to access the options that are now in that menu
I disagree. It was annoying to always have to delete the screenshot photos that you really only wanted to have on the clipboard to paste somewhere, or only wanted to extract text out of. I was very pleasantly surprised when the new options were added, and I regularly make use of the different available choices.
Instead, what I dislike is that you can’t keep the screenshot dialog open in the background. It would be fine for screenshots to go straight to photos if the screenshot dialog was still available from there for each individual screenshot taken (including the options under discussion).
That would turn it into an app, but on iOS there’s no way to draw UI elements on top of other apps.
As I wrote, it could be integrated into Photos. Or they could make a Clipboard app that integrates it. Apple isn’t foreign to turning OS-wide functionality into apps, like Files and Passwords and Preview. There’s also functionality made statefully available via Control Center and Notification Center, which do “draw UI elements on top of other apps”. There’s various ways this could be accomplished.
> everyone was perfectly fine
This was never true, of course. You've slipped way down the slope of the mythical golden past.
But also, having the option not to show an empty menu is a trivial part of customization, so this is also solved in my suggested approach.