In the British military we are taught to shout grenade when throwing them too.Two military things that drive me nuts:
1. When the Sarge character yells, "Lock and load!" In anything taken place in WW2. Actually, in WW2, it was Load and Lock! It refers to putting the en bloc clip of eight .30 caliber bullets into an M1 rifle. You pushed them all the way down inside the action (load) them snap the bolt forward to engage the first bullet (lock).
2. When throwing a grenade, someone yells, "Grenade!" when that's for only one when one has landed among you that you might want to get out of the way of. You actually yell, "frag out," as all US grenades are fragmentation by nature.
They also never get the explosion of one right in movies. Modern frags go off with a puff of smoke that looks sort of brown with a slight purple tint. I ran a grenade range once and watched several go off from the tower with it's very thick armored glass view port. I left that position when a piece of shrapnel came right for my head and scratched the glass right where the space between my eyes was. Without that glass, I'd have died with just enough time to think I realized it was coming. Anyway, even most people who've thrown them have unlikely watched them go off several times, I'd think.
We are also taught to watch where it roughly lands but you don't stay there admiring the bang, so I agree with you there that unless someone was being rather silly, or just wants to push their luck, they won't look out for it going off.