My 920 had the same issue, exactly like the overheating issue. Looks like MS/Nokia didn't learn from its past errors... already had the same problem with my nokia N9 before that.
A screen protector shouldn't be necessary. If you take care of your phone, it shouldn't get scratched. Of course, an accident can happen but like others, i do not want to put a screen protector and feel that cheap plastic when using it. Paying a $500 phone to put it in a $5 case and put a $10 screen protector on it... i still don't really get that but to each his own. ��
Besides, screen protectors can sometimes damage the screen even more because of the dust that can be under it. The screen protector on my 920 caused some serious reactivity issues, especially on the startscreen. On the other hand, a glass screen may slip on some surface while the plastic screen protector will act like a grip and get scratched, and that may damage the screen where the glass would have been flawless.
And once again, in the past 5 years, i only had issues with nokia screens... Apple, samsung or even iRiver screens never got scratched of were prone to finger prints while all my nokia devices suffered from micro scratches or oleophobic coating that wears off pretty quickly.