Ok, I appreciate the many reasons a lot of travelers do so or do not make reservations. Trouble with this is, while you will likely find a spot, will it be what or where you want or whats leftover.
In every camp i've visited when they are in 'season' this is normal, the early bird always gets the best. Drive ins get the leftovers.
By reserving well ahead you have opportunity to choose the best of sites that relate to your wishes.
In the central west, hours drive away from big cities weekdays are as busy as weekends. This is summer vacation country,not weekend busy, weekday empty.
Plan ahead where you can to assure your family their best experience.