Yes, screen protector is necessary for smartphones to avoid screen damage from phone drop and day to day use.
I am giving this answer based on my experience.
I am using 2 smartphones, one with screen protector and another without screen protector.
You also noticed that the phone screen gets light scratches with 4-5 month use (with and without screen protector).
In this case, if your phone has a screen protector, then you can replace it with a new one, to get a clean screen again.
Recently, my phone dropped from my hand and it’s screen cracked. When I saw the crack, I noticed that the screen touch feature was working and only glass was broken.
In this case, crack is only on the screen upper layer and can be avoided, if the phone has a screen protector. But, now I have to replace the screen, which definitely costs me more compared to screen protector.
So, if you are comfortable with a screen protector and like to protect your phone screen from light scratch and simple damage, then a screen protector is always a good thing to use with iPhone and Android phones.