Let $k$ be a field of characteristic zero.

Let $X$ be a finite type algebraic stack over $k$ with a coarse (or good) moduli space $M$.

Suppose that $M$ is isomorphic to a point, i.e., $M = Spec k$.

Examples of such stacks are classifying stacks $BG$, with $G$ a finite type group scheme over $k$.

Are there any other examples of such stacks? What if we impose extra conditions on $X$ such as smoothness, affine diagonal, etc?