The answer to the OP's question has two aspects, depending on which way you interpret the question.
Biologically speaking, yes, type 4 hair was designed to grow and break off at a typically shorter length, based on its chemical structure and growth rate. That is because most peoples who had type 4 hair lived in the hot, harsh climate of sub-Saharan Africa at the time we developed into the different races, and it was Nature's way of keeping our most vulnerable body part (our brains) protected against the insulating effects of a straighter, more fur-like hair texture. That is also why the further north you get, the straighter (and more fur-like) human hair becomes. Ever notice how cool your head felt if you ever rocked a TWA, even in summer? It's because our hair grows up and away from our scalp, not down, allowing for air to circulate through to our scalp when our hair is short, keeping it cool.
Now, if you're thinking in terms of "it is destined to be short, so why try to grow it long," then no, type 4 hair can grow as long as our bodies allow it to. As humans, we have learned to manipulate our environment to suit our whims, and that includes the functioning of our bodies. We have learned techniques that can help us work with our hair to make it look its best and grow it as long as we want, but
what keeps messing us up is that we are still trying to use techniques/standards/products meant for types of hair other than our own.
No matter what we do (and I relax my hair mind you), we do not have type 1, 2, or 3 hair (most of us, anyway), and
using methods that work for those types of hair will not work for us, nor make our hair look like those types of hair without destroying its health and integrity. Our grandmothers knew this (they were told this rather consistently, albeit in very harsh ways), so they were not abusing their hair in all the various ways that we do to make it look like what it's
not (i.e., straight). They kept it up and out of the way, to grow however it did, usually long from the pictures I've seen.
It wasn't until we started pressing, then konking, then relaxing, then greasing and gelling our edges, then weaving the hell out of our hair to make it look like other races' hair did it start to get shorter and shorter. And now that the natural hair movement has taken hold and given us back more of the knowledge and understanding we once had of our hair, the pendulum has begun to swing back to where some of us are realizing our hair's full potential, regardless of the way we choose to style it. I relax my hair, but I know now that relaxing it does not mean I can treat it like natural type 1, 2 or even 3 hair--
it is still and always will be type 4 hair, and once I learned how to properly care for my lovely, kinky hair, it has rewarded me with the length I have desired. 
Does it mean I have to take more time with it? Yes! Does it mean I have to baby it more than other types of hair (especially since I damage it with relaxer)? You bet! Does it mean I can't wear it down every day and manipulate the hell out of it with combs, cuts and color like my straighter-haired friends? Most definitely! But I wouldn't trade it for the world, because it is healthy, it is unique, it is beautiful, and it is all mine.
I've been natural, relaxed (currently), braided up, weaved up and dyed if that helps.
