The MBTI is mostly just useful in that it's one of the few things that actually sorts humans in a hyperdimensional way, which is really how we're best categorized.
We're all slight wobbles (well, statistically speaking) around the center of a like 20-100 dimension distribution.
MBTI is basically just PCA on that space in to a 4-dimensional one, and while we can argue how evenly its bucketing split the actual distribution of people (not ideally, but not terribly), or how much information was lost in that downcasting (a lot!), I think the basic premise of viewing people as a composite of slight differences across many dimensions is a useful viewpoint we don't normally engage in.
So if you could pick 16 LotR characters that form a hypercube of traits, then assigning LotR characters is the same as the MBTI. The problem is usually that LotR quizzes and the like are a) much smaller than that (4-8 characters) and b) not laid out in a hypercube (ie, there's not 4+ dimensions of wobble, there's 2 or 3).