Only if you're using "proper tired" to mean exhausted. Restlessness does not only come from not being tired yet. It's entirely possible to be very very tired and yet restless. It happens to toddlers, it happens to older people, it happens to people with all sorts of medical conditions. Trying to keep going until exhaustion outweighs all those other issues is really hard on the body and mind. Waking up with tingling extremities, stressed muscles and joints, or even permanent nerve damage because you slept in a bad position isn't so great either.

Maybe tiredness, relaxation, and ability to sleep are all in sync for you. Good for you. I remember when I could have said the same, but I never made the mistake of assuming that my experience was everyone else's.