It would be possible for a natural curvature of spacetime to appear as dark matter. Dark energy can be described in this way. Putting dark energy on the right hand side of the Einstein equation interprets it as matter/energy while putting it on the left hand side interprets it as a geometrical property of spacetime.

The problem with dark matter is that it is uneven. For example the observations of the Bullet Cluster suggest there are concentrations of dark matter that (before the collision) corresponded to the visible matter density.

When describing the expansion of the universe as a whole we could model dark matter as a geometrical property, just like dark matter. However this wouldn't help us explain the observed unevenness in the distribution of dark matter. That can only be explained by putting the dark matter on the right hand side of the Einstein equation i.e. as some form of weakly interacting matter scattered around the universe.

One last point, the flat geometry actually seems most natural to most physicists. That's because if the universe is curved that curvature changes (increases) with time. If the universe was even slightly curved just after the Big Bang then it would be massively curved now - 13.8 billion years later. However if the universe started flat it stays flat. Since the universe obviously isn't massively curved right now the simplest explanation is that it started flat and therefore has remained flat.

It would be possible for a natural curvature of spacetime to appear as dark matter. Dark energy can be described in this way. Putting dark energy on the right hand side of the Einstein equation interprets it as matter/energy while putting it on the left hand side interprets it as a geometrical property of spacetime.

The problem with dark matter is that it is uneven. For example the observations of the Bullet Cluster suggest there are concentrations of dark matter that (before the collision) corresponded to the visible matter density.

When describing the expansion of the universe as a whole we could model dark matter as a geometrical property, just like dark energy. However this wouldn't help us explain the observed unevenness in the distribution of dark matter. That can only be explained by putting the dark matter on the right hand side of the Einstein equation i.e. as some form of weakly interacting matter scattered around the universe.

One last point, the flat geometry actually seems most natural to most physicists. That's because if the universe is curved that curvature changes (increases) with time. If the universe was even slightly curved just after the Big Bang then it would be massively curved now - 13.8 billion years later. However if the universe started flat it stays flat. Since the universe obviously isn't massively curved right now the simplest explanation is that it started flat and therefore has remained flat.