No. Apple didn’t force you to put a screen protector on your phone. That was voluntary on your part.
If Apple’s responsible for this then how far does it go? Should Apple then also give you some sort of compensation for the fuel you expended driving back to the Apple Store that you otherwise wouldn’t have had to if your phone was not defective? What about the general wear and tear on your vehicle for the extra trip? (Or if you don’t drive then the cost of the bus/subway pass for the trip.) Or perhaps they should compensate you for your time. Maybe you had to take off work a bit early. Or you gave up something else to go to the Apple Store to return the device.
You claim it’s ‘not uncommon’ to receive a defective phone these days (I’d like to see some proof to back that up but that’s not the point here) so why not wait to put a screen protector on until you know you have a non-defective phone?
You’d probably have better luck just sending a polite email to the screen protector manufacturer and explain the situation. As the other commenter said, these things are cheap. I’d be willing to bet that the manufacturer would be willing to send you a discount or even just a whole new protector for the sake of brand goodwill.