My son, went to no naps once he was in Kindergarten.
But even in Kindergarten, they had naps. For the first part of the year.
My son would be tired after school and would nap at home too.
But due to homework and other schedule issues, I couldn't have him nap everyday, which is usually what he would do.
He is a regular napper.
But once he started Kinder, then naps were not possible.
Even my older daughter, would nap, after school at times, even when she was 7.
Now they are 6 and 9, so they no longer nap.
But sometimes need to.
Also though, some kids get seemingly "hyper" when tired or overtired.
My son, is like that. WHEN he is tired or overtired, he gets more "hyper." Because he is trying to FORCE himself, awake.
Times when my kids can't nap and are tired, they go to bed earlier. AND DINNER & showers is also, earlier.
With no battles.
They know themselves and their cues, and I do too.
I always give them, a head's up, prior, that "today, you both are overtired, so bedtime earlier..." and they don't fight it.
They know that too.
I make the house dark and quiet, about 1 hour prior to their actual bedtime... IN ORDER to, wind them down and key them down.
It is necessary. To create a calmer atmosphere, BEFORE the actual bedtime.