Why did the edge of Olympus Mons collapse? On Earth, the maximum height for a mountain is ~10 km. Beyond that, the mountain will start to spread or collapse. On the surface of Mars, the gravity is not as strong, so the maximum height for a mountain is higher.
The edges of Olympus Mons are very steep cliffs, rather than being a shallow slope all the way down. Surrounding the mountain, there is a large aureole that looks like it might be left over from landslides.
Did the edges of Olympus Mons collapse and cause a landslide because the mountain reached the maximum height for Mars? Or was some other process involved?
This source from NASA says:

Most scientists think the the cliffs formed by landslides. This collapse is driven by the weight of the huge volcano exceeding the strength of the rocks it is built of.

In other words, one theory is as you have surmised: The outer 7km shell of the volcano appears to have slid down, all around the mountain, forming the cliffs.  This paper has more information.
Another theory says:

The part of the Olympus Mons edifice surrounded by cliffs is morphologically similar, albeit at a much greater scale, to the volcanic seamounts on Earth like
the Canaries and the Hawaii.

This says that the Hawaiian volcanoes have a similar cliff around them, so perhaps Olympus Mons was formed in an ancient sea.  This paper by the same author gives the reason for why the cliffs don't go all the way around as more evidence for a sea on the portion where the cliffs did form.  A third paper by this author states that this also explains the aureole extending out so far.
A third theory is that as the lava and ash spread out from the volcano, eventually they reached a point where rather than forming rock they more formed sand dunes - which eventually started to blow away.
So, in summation, it could be because the mountain is too tall; because the bottom 7km or so was underwater as the volcano was forming the mountain; or because the outer portion of the mountain was only formed as ash.