There's probably a few reasons, really...
First and foremost, children really don't "know" themselves, nor do they have any real inclination or desire to do so. They know whot they want, but not why they want it; the why there is irrelevant to them. A baby screams because it wants food; it doesn't care about the specifics that it's hungry, or whot hunger means, it just knows it wants to not feel in pain anymore. So, too, does this carry over to psychology... they know whot they want in life, generally "to have fun" or "a million jillion ice cream cones". Past that, they don't see much reason to understand their motivations behind such, or the mental processes that led them to such a desire, because it's irrelevant to them.
Adults, conversely, have developed their brains farther, as well as their social requirements. Most adults aren't really any better than children, honestly though. In my class at school, we had to do similar stuff, not MBTI directly, but same general concept... noone cared, they didn't see any connection between how they understand themselves and others relating to being capable of working together. MBTI and all other personality tests are just an attempt to quantify and explain the way the mind works, for ourselves, and others. If we understand how we think differently, and how we interact due to such, we can take advantage of this understanding and use it to better ourselves and those around us. Most adults don't progress past childhood in that manner, however. They know whot they want, and don't care why they want it. If yeu knew WHY yeu wanted it though, yeu might not need to continue to want it; or may find better ways to sate that desire indirectly.
There's also the matter that, as adults, we've been conditioned through school, government, parents, society as a whole, to classify and structure things, rather than understand it. The question of a child is "why?", the question of the adult is "where does it go?". It's strange, then, isn't it? That those who are least able to utilize the answer to 'why' are the ones most interested in asking it? Whereas those who could make use of such information, have been systematically conditioned to avoid such.
Strange stuff really.
But anyway, adults tend to try to rationally explain their world; the human brain is designed to create order from chaos anyway. As yeu grow older, it gets better at doing so, and doesn't accept "no clue, it just does!" very well anymore. If yeu look at a cloud, yeu can see 'order' appear... faces, shapes, whotever, clouds turn into things because yeur brain tries to craft order from chaos. As we progress, we are taught how to create order by labeling things into nice, tidy little bins. If it has a name and a number, then it is ordered.
Take for example, even myths, legends, and religions; many of these exist merely to explain that which we can't understand. Alot of the bible isn't direct religion, it's just mythology in large portions of it. Any time yeu see something explained by rather fanciful reasoning, it's generally just something people didn't understand and are trying to make sense of. The whole thing about like... how snakes have generally lost their legs, but some have vestigial remains, is explained back in the whole adam & eve story. It's not likely that happened at all, and it wouldn't make any sense anyways, since it'd require god to be an idiot for that to have occurred in that manner.
But anyway, these things are meant to explain things in an ordered sense. As we grow older, we require more in depth explanation. For a child, it's alright to just know "I don't like her >=O " but never have a reason as to WHY yeu don't like that person. Scoot forwards 20 years, and yeu want to understand whot exactly it is about her that yeu don't like. With that additional definition and clarification, yeu can perhaps learn to like her, or understand why certain behaviours irritate yeu and can recondition them to no longer exist. A child can't do that, usually.
So why don't kids need MBTI? Because it's abstract enough they can't understand it, because it doesn't hold direct relevance to their desires that they can see, and because they really don't need to know the intricate details of their own mind or others. They just don't care.
And so, they don't really value it. Because they have no need to understand themselves or others around them.
When they require that need, they'll explain things in their own way, whether it's through religion, MBTI, some other psychological profile, or whotever. They will order and categorize people as required.
For their age, however, all they need is "Nice, bully, mean, whiny, tattletale" and several other broad reaching terms that don't really accurately describe the person as a whole, merely just key aspects they've noticed.
They do still categorize people, obviously, it's just not as in depth because it's not required.