Aside from the points raised in nbro's answer, I'd like to point out that for a single MDP (a single instance of a "problem"), it may be sensible to study it from perspectives that include no policy at all, or multiple different policies.
For instance, if I have an MDP, I may be interested in studying it by looking at various inherent properties of the environment. And if I then have multiple different MDPs, all without any policies or anything like that, I could compare them based on those properties. For example, I might simply want to measure the sizes of the state and action spaces. Or write out something like a game tree, and measure properties like the branching factor and the average / min / max / median depth at which we can find a terminal state.
On the other hand, it can also be interesting sometimes to study multiple different policies all for the same MDP. A very common example would be any off-policy learning algorithm (like $Q$-learning): they all involve at least one "target policy" (for which they're learning the $Q(s, a)$ values -- usually the greedy policy with respect to the values learned so far), and at least one "behaviour policy" (which they're using to generate experience -- often something like an $\epsilon$-greedy policy). A more complex example would be population-based training setups, like the one DeepMind used for their StarCraft 2 training; here they have a large population of different policies that they're all using in a complex training setup (and technically I suppose we should say they also have many different MDPs, where every combination of StarCraft 2 level + training opponent would formally be a different MDP).