As @Hanzou 's post below mentioned, advancing in the MA's should never be about getting the next stripe or color. It is about learning. Motivating kids through getting another stripe, color, button, etc... especially every few weeks is a big part of what is eroding the quality of MA as a whole. IMHO . It that is all a person has ever seen it is hard for them to understand there is a much better, quality way to learn.
Don't assume that doing things the "old school" way is necessarily higher quality or better. Often times, people are looking at the failures of the "old school" way and trying to find ways to improve on them.
FWIW, I've been teaching TKD since 2012 and this age group specifically for about 5 years. When I started teaching at my old teacher's school, we just taught the preschoolers the same as all the other kids, with the same belts. After Mr WaterGal and I started our own school, we decided to put the 4-5 year olds in a separate class, but to keep the same belts and curriculum, just taught differently. This approach mostly just meant fewer distraction for the older kids (not that that's a bad thing, lol). We went with this approach for a couple years, and had a few kids make a lot of progress, but most of the kids had a high turnover and didn't get very far. Then, a couple years ago, I started doing more research into child development, how other schools taught this age group, other ways to structure curriculum, etc, and we totally revamped the program. Now, our typical retention for this age group is over 1 year. While a few of the kids could probably have advanced a little faster in the old way, for most of them, they're getting a better quality of martial arts education now and staying for longer. Part of that is getting their own belt system, though that's only one part.