You need some source for minerals for nutrients for those reefs.
If there is no exposed landmass to erode, this becomes a bit of a bother.
You need to explain why you have large areas of shallow-ish water, with sufficient nutrients for abundant life.
And you need to explain why your reefs do not form coral Island that protrude out of the water.
As for having vast reefs but no coral islands: no problem.
Your coral-equivalent grows at any depth from several hundred meters down, up to but not reaching the surface. Something as simple as the local star shining with severe UtraViolet light, that sterilizes the surface but is absorbed and neutralized by a few meters of water. This will allow the coral to grow towards the surface, but stop it from reaching the surface.
Add that to a world that has smaller tides, so there is no great sloshing of the waters to expose the coral, or to wash coral sand into piles that become islands.
As for not having real landmasses, with mountains etc.. You just need to not have active plate tectonics. Your planet is Old, the crust is many hundreds of km thick, and locked in place. Anything that pokes out of the water is already eroded down.
As for the nutrient source...hmm.
Maybe your thick crust is being invaded by the ocean, causing multiple persistent but non violent geothermal vents all over the place?
Or.. a bit radical but picturesque:
You planet HAD a medium sized moon, in a very low orbit.
The ridiculous tides from this is what scoured the landmasses down to sealevel, and also filled in most of the ocean deeps.
Now, this moon has passed below the Roche limit of your planet, and has broken up into a very dense ring system. Very pretty rings, their even mass distribution has completely stopped the tides allowing your reefs to form, and the continual drizzle of dust falling from the rings seeds the oceans with ample nutrients.