Because the planets have to form first? The Lagrange points don't exist in their own.

The Lagrange points are only stable as long as the object in them is much, much smaller than the planet is. Once it becomes large enough to be exerting gravitational influence of its own the Lagrange points become unstable and it drifts out.

I don't think it's widely accepted as plausible any more, but I recall reading a theory that Theia (the planetoid that impacted Earth very early in the solar system's formation to cause the formation of the Moon) formed in one of the L4/L5 points in exactly the manner you're proposing but then collided with Earth once it got too big to remain stable there. IIRC more recent simulations suggest Theia had to hit at a higher velocity than this scenario was capable of producing, so that's why it's been deprecated, but the formation-then-instability bit is still valid.

Matter would have to accrete equally at six equally spaced points, which as others have pointed out has a problem with getting started in the first place.

The other problem is that a protoplanetary disk is not uniform, so even if by some miracle, six things of equal mass started out at six equally spaced points along one orbit, one of them would almost certainly accrete more mass than the others.

That would throw the Lagrange points out of alignment, if not also slow the orbit of that body, and I imagine that would quickly lead to runaway loss of equilibrium.

You are free to imagine them going on to happy existences in separate orbits, perhaps with a sweet system of resonances around the star, but something tells me that's unlikely.

On the other hand, there's a neat fiction story in there somewhere if you want to apply it to our own inner planets. Mercury, Venus, proto-Earth, Theia, Mars and the asteroid belt happen to number exactly six.

Manually positioned planets sharing an orbit is hella cool as a scifi concept, maybe as an early dyson sphere precursor.