As an admin, alter the default settings so that the cutoff date is 0 days after the due date and enabled, and require students to use the submit button. You could also adjust the language pack to ensure students are given a reminder to click the submit button - but this leaves the option to upload as a draft for further work, or for multiple file submissions.
That way the cut off date IS set to the due date by default and would need to be specifically changed or disabled. If the submit button is constantly off screen, you could also try looking at some theme code to make it float at the bottom of the screen as some themes do with settings page 'Save Changes or Cancel' buttons.
These are admin options that set the default for a specific institution's teachers. They do not (other than the theme suggestion) involve changing code, so have no problems for upgrades and the settings are already there in Moodle, so really there is no need to make further changes to the main code, or for teachers to have to remember to change settings for every assignment - just a one-off admin setting change and its done.
So hopefully, you can relieve your 'shock and horror', by an investigation of manipulating already existing site settings!
PS. for many other institutions, that difference between due date and cut off date is an essential requirement as students are allowed to submit late and can submit with extenuating circumstances even after other student work has been graded.