Gotta snigger as at 3 my own DS was the perfect pupil - top scores on all his eyfs tick boxes, used as the example pupil for ofstead, new parents viewings, staff training etc. The ideal performing monkey poor love, he could even read "cat sat on mat" level books, was polite, sociable, shared his toys kind, yada yada. As a toddler he was almost too good iykwim.
Age 4.5 when he started school, it all fell apart. He wound up being one of the 1.5 kids that has a statement due to complex needs and can't cope in mainstream at all. He's 3 years behind academically now too. Many children with issues like dyspraxia, dyslexia etc can only be effectively diagnosed at about 7 - yet these are the types of disabilities that can severely drag down the academic progress of even the brightest child.
3 is WAY to young to do anything but weed out the most obvious physical disabilities in the children & any crazy loon parents. Sadly not all private nurseries are in buildings properly adapted to take the full range of physical disabilities, or have the funds to make the adaptations that might be required.
Sending in a kid who is not past the 48 D&V vomiting rule risks that kid being sick on the carpet and firmly demonstrating the parents come under the crazy loon category & thereby causing the staff to heave a sigh of relief at having dodged that bullet when they send out your rejection letter.
As a point of principle I deliberately chose a nursery that had as wide a range of children from different backgrounds, and a few with disabilities too. That's because this is the age to teach tolerance, kindness, sharing and all those compassionate qualities that basically make people more likeable, altruistic and socially successful in later life.
It paid off as my lad was later diagnosed with ASD traits so that early emphasis on socialisation was far,far more important than I realised at the time & is the reason why I think he manages to make friends in most environments despite his disability. The sign language he learnt in his eagerness to communicate with everyone also helped his language development in a way I didn't understand till much later. At the time I just thought it was nice that he was learning to be inclusive in his friendship group.
As parents we need to nurture the whole child, even when we are lucky enough to give birth to a genius. Sadly many truly gifted individuals do not have the happiest personal and emotional lives and that's important too.
Oh and most parents want the best for their kids. It really is only a teeny,tiny minority who don't. That's a true fact across all races, socio-economic class and nations, and has been since the dawn of time.