I don’t think your DC should sign anything that they are not comfortable with. The wording as you have represented it (“anything they may create after leaving the company that’s “related” to any “subject” the employer currently covers or may cover in the future”) is overreach and not only would create problems for your DC down the line, but also is something that would at least theoretically have to be disclosed to future employers.
In reality, it probably would never actually come up, unless and until your DC creates something that starts bringing in a lot of $$ and then suddenly the old employer will pop up and want a piece of the action. And then given costs of litigation, nine times out of ten it makes more financial sense to reach a financial settlement than to fight a court battle. But I can see it also being a problem if your DC wants to register a copyright or seek a patent somewhere along the way as well.
So no – if the company wants to protect its trade secrets or have an employee enter a non-compete agreement, that’s one thing – but I think trying to lay claim to anything that person may do on their own in the future is way out of bounds. I know it may be very difficult for DC to walk away from this job offer… but I think you have to conceptualize this as something that in itself has monetary value. In this case the company may be paying their employees $X but if they are asking for a potential $XXX in return, it’s a problem.
Also, the employer’s statements that they “didn’t understand the legal stuff,” but “everyone else signed it” so it was a take it or leave it deal – is really not acceptable. Or at least it’s a very good reason to “leave it”.