No, why should it be meaningless? It's an important topic. Mixed states are needed to make QT complete. It's not only that it's needed to describe situations, where you need a reduced description, like in many-body physics, where it's simply impossible to describe 1 mol of some matter (i.e., about ##6 \cdot 10^{23}## particles) in all detail. This is as in classical statistical mechanics: you cannot describe all details, so you try a "coarse grained" description of some "relevant degrees of freedom" in a statistical way. E.g., to describe a gas you don't need and cannot describe all the trajectories of each particle, but you rather want to describe it in terms of some "macroscopic" properties like the density, the fluid velocity, temperature, pressure etc. Then you use a coarse-grained description. In thermal equilibrium you then use the Maxwell-Boltzmann distribution or the corresponding quantum version, i.e., the microcanonical, canonical or grand-canonical statistical operators.
In addition you also need it to describe parts of a composed quantum system, even if the complete system is in a pure state. That's particularly important if you have to deal with "entangled states", which is a truely quantum property with no analogue in classical physics. Take e.g., the spins of two electrons in the state with total spin 0, i.e., with the state vector
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle -|-1/2,1/2 \rangle).$$
The true unique description of the state is then the statistical operator
$$\hat{R}=|\psi \rangle \langle \psi|.$$
The question now is, what's the statistical operator for the spin of one of the electrons? That's given by the "reduced statistical operator", defined by a partial trace, i.e.,
$$\hat{R}_1=\sum_{\sigma_1,\sigma_1',\sigma_2=\pm 1/2} |\sigma_1 \rangle \langle \sigma_1,\sigma_2|\hat{R}|\sigma_1',\sigma_2 \rangle \langle \sigma_1'|=\frac{1}{2} \sum_{\sigma_1=\pm 1/2} |\sigma_1 \rangle \langle \sigma_1|=\frac{1}{2} \hat{1}.$$
This means that in this pure state of the two electrons the single electron is unpolarized, i.e., it is not in a pure state. That's characteristic for entangled states.