The main problem is that it takes longer. In between the vaccinations, your child is not vaccinated against each disease. It becomes a danger to other people if it contracts the diseases, apart from the risk of contracting an ailment in the interim.
Why jab your kid in the arm three times more than you need to? It is unlikely that autism is caused by an 'overload' of the immune system, if your child has a cold, diarrhoea and an infected cut do they become autistic? No. Yet these three infections are much more challenging for the immune system than the manufactured immunogens in a vaccine. Isn't the 'overload' theory in direct contradiction to the argument for measles parties?