As far as I am aware the coloured belt system developed to encourage children in what was then becoming a 'sport'. This also helped its export to the US. I think coloured belts are useful for children, especially in aikido where it takes alot of patience to reach some degree of proficiency.
The whole idea of a grade system is a modern invention. Traditionally you would be taught martial arts individually or part of a select few. No grade would be awarded, you would just complete the training and when your teacher felt you were good enough to instruct you might end up with an instructors certificate.
Obviously everything has changed now and martial arts on the whole are taught in classes where anyone can join. Especially in the more sports orientated martial arts and martial arts directed towards childern for health education the grading system assists with competition (so similar level students can compete) and encourages people.
I think grades are useful in aikido because it helps people formalise what they know, and people can work towards gradings and feel confidence in certain techniques once grades have been achieved. However I think in many cases the full knowledge and experience of an instructor is rarely passed over to students now since there are several students at different stages of development, may of whom won't stay with the instructor to the point of being able to teach themselves.