No definitely not!
I have one past that age and one not yet there (15)
Eldest (20) is currently at Uni, where we pay his rent - he pays his bills/living costs.
We expect him to come home short term once Uni finishes, and we may choose to charge him a small amount of rent, but I expect unless our circumstances change, we will probably save that money.
I was charged rent at the same age, which I was happy with. It was a fairly nominal amount I seem to remember.
I then moved out with my then boyfriend and ended up pregnant at 22. The relationship broke down quickly (he was a dick) so I moved back home. I went back to work when DS was 3 months old (he came to work with me - nursery)
My parents charged me a large amount of rent. Now I appreciate that's their right, but they charged me so much that there was no way I was ever going to be in a position to save to move out (I had to use the rest of my money to feed and support us both). Don't get me wrong, I was grateful that they put a roof over my head, but it almost felt a bit controlling - like they were making sure we couldn't make a life for ourselves away from them. Financially they didn't need that money either. It was the principle to them (they were very honest about that)
It left me with a distorted view of charging your children rent. I always swore I'd never put my own children in that same position - not that I wouldn't charge them anything at all, but a realistic amount so that the young person can work to make themselves independent.
For clarity, they took about 75% of my wages.