Are screen protectors even needed these days (for scratch protection)? I've gone more than a year without one on my 5S and have no visible scratches. With the hardened glass on the 6S, this should be even less of a concern.
There's two answers to this and you're not going to like either:
1) Yes - In the same way you should always wash and wax your car daily. The coating on the iphone/ipad screens will wear out at some point which will make cleaning the screen harder, and using "screen cleaning" solutions will wear it off faster. So the screen protector prevents the original screen surface area from wearing. The cost to this is that the screen protector may actually not protect the screen from anything and you're only keeping the resale value higher provided you don't scratch the rest of the phone. My old Nokia phone has one, and I found it a pain in the ass to remove after, so you may damage the phone more by trying to remove it.
2) No - If you don't have a screen protector (my iPad(3) doesn't have one) the screen won't get damaged at all unless you use a blunt (eg plastic) stylus on it. My iPad is completely scratch free, but the finger prints that get over it do get rather annoying, and that would happen with or without the screen protector.
My suggestion would that you should only get screen protectors for devices that are meant to be used by more than one person. Like employees (who might not treat their employer equipment as good as their own equipment), children ("trouble" children won't care because Mommy or Daddy will just buy them a new one), and disabled people (who might otherwise be unable to care for the device properly.) If it's your own personal device, you can decide if the hassle of dealing with the screen protector is worth it. For a "phone" it might be better to get a "sock" or bumper, as dropping the phone is more likely to shatter the screen, protector or not, depending how it falls. If a phone falls flat on it's face, the force of hitting the object will go straight through the screen protector anyways.