Notes that ships with iOS actually has a nice document scanner built in that uses the phone camera ... I mean it does the transform you describe to get better-than-normal document photos.
Too bad it then simply adds as an attachment to the note and doesn't allow you to go straight to Share.
There are other apps that do similar things. When I was in college a decade ago I was using "CamScanner", which seems to still be around (though I feel like I read recently that it got bought and the new owners started doing something sketchy)
These days I just use the regular camera app. Documents are plenty readable as-is, and you can straighten/adjust 3D perspective/raise contrast using the regular photo editing features (at least in iOS)
Just tested this. It takes four click to get the the share screen after a capture. It does not requiring switching apps so it is fairly quick:
1. Click Save in bottom right (segues to note)
2. Click scan in note (segues to edit context)
3. Click share in top right (open share menu)
4. Click method of share for pdf (sms, email, copy)
But wait! You can use the press and hold (3D touch / force touch?) to skip no steps!
1. Click Save in bottom right (segues to note)
2. Click and hold the scan in note (3d touch pop up)
3. Click share in the pop up (open share menu)
4. Click method of share for pdf (sms, email, copy)
Too bad it then simply adds as an attachment to the note and doesn't allow you to go straight to Share.