I've had mine for almost a week without a screen protector and have yet to see a single scratch (at least any noticeable enough to see). Still will get a screen protector though but I do have to give props for how finger print resistant the screen is, and since it's plastic it's unlikely to crack.

There are no sharp edges on those plastic parts in the slot, they are rounded ( at least a little bit). If you put it in and out just normally without interpreting The Flash there is nothing to worry about. I'm not even careful when taking it out and putting it back in, I just do it. Nothing happens. Besides, why would someone slamdunk it into the dock, anyway? I think it should be common sense that if you treat your stuff like shit, your stuff's gonna look like shit sooner or later.

The Vita screen is plastic as well. 

Plastic doesn't shatter, it's better for kids that way, a scratched screen is still usable a shattered one is tough. 

From what I've been reading, most people haven't scratched their screens yet, but better to be safe and get a screen protector

nope. I have screen protectors on order as well for my and my son's switches. I didn't even realize it wasn't glass, but the little bit I've used the touch has been super responsive and it looks great, so meh.

As I mentioned in a different post, I put a Hori screen protector on mine day one and I havent seen any evidence of markings on that whatsoever.  However,  I have noticed an ever so slight vertical mark on the back left of the unit where one of the rails would be.  Could possibly be from the dock rail....or not.  Will have to watch it I guess.

Nope, I bought a tempered glass screen protection for it

Wha-??? I had no idea. Personally I'd actually prefer if all devices just came with plastic screens rather than glass. The so-called "scratch resistance" of Gorilla glass is joke. Dust in your pocket can easily scratch it, and the scratches have an unholy rainbow coloring when the screen is on. Nasty, nasty stuff. If  I'm gonna have to use a screen protector anyway, better that the built in screen is shatter resistant 

That said, do like the feel of glass, which is why I hope for a glass screen protector.

Breaks my heart watching someone intentionally breaking a console :(

according to the first linked video in the OP the screen has a Mohs hardness of below 3 - finger nails are at ~2.5 on that scale and I very much expect the screens scratch hardness to be above that, so I guess it's at ~2.8

that's a pretty soft surface that will give in to friction applied by any kind of common metal alloy and many common dust particles