The coarser grit will cut more aggressively, so the process is faster with them. The grit breaks down fairly quickly, so even if you start coarse, one ends with a finer slurry until you refresh it with fresh grit.
I suppose finer grits are preferred with finer stones because otherwise the surface would be left all scratched up. I should point out that on softer stones than a typical washita, using the coarse (around 90x) grit leaves a very rough unusable surface, in my case they were a slate, and some waterstones. After the coarse grit, I used finer grits until a uniform surface was achieved.
I have about a couple dozen sharpening stones, mostly washitas. The fine ones are Arkansas (Dan's and Norton) and those came my way in good shape, so I didn't need to lap them. Some of the washitas, indias, crystolons arrived in need of some lapping. The infrequent need to flatten and trying to wear them evenly is one of the reasons I prefer the washitas and the Indias over water stones.
Maintaining oilstones or waterstones with a diamond stone should work, the amount to remove is small compared to what's needed when they're dished or clogged. It's in that case where the coarse grit saves you time.
There's one last point to be made. Once you start using a relatively low wear oilstone like an India, washita or an arkansas, the roughness left from the manufacturer's lapping or your own refurbishing lapping wears off. I think they say that the stone "has settled". It's around that cutting power that one works with when using these stones, not their behavior freshly lapped. One could rough them up with a coarse stone, but that just adds time to the process and may not be needed.