If I had to have one stone at home for J knives, it would be a medium-finishing stone, and the aoto is okay for that. This assumes I don't chip my knives, need to thin, or need to grind a fresh edge. If that's the case, then adding a 1k will cover that. Then I would get a finishing stone finer that the aoto.
I have a kouzaki aoto that is kinda muddy. After sharpening there's leftover mud that dries to a brownish dust even though the stone is dark blue, and while sharpening the mud and stone is a dark grey-blue. I leave the mud from the last sharpening on to help start the stone for the next session.
I agree with what Grunt173 said about mud.
The stone leaves a really serrated toothy-refined edge because it's on the muddy side and it's a natural stone. The particles kind of make sawteeth within sawteeth as the particles fracture, especially since the mud kind of suspends them to do that more easily. I use it to give that kind of edge which I like more that the equivalent synthetic at either end of the grit range for the aoto. But yeah, for the cutting speed, synthetic stones are usually better. I have ones from JKI, and if I were in EU, I'd get the ones from JNS.
I would get a fine Japanese natural stone because they are splash and go, and that's convenient for me, and I like the edge more than the equivalent synthetic. The natural stone is usually harder and heavier than the comparable synthetic. I'd get muddier if I wanted a wide range of serrations, or harder if I wanted I wanted a more narrow range of finer serrations for the edge. The edge is by no means "serrated" in the naked eye visually like a saw, it's just how it feels, and what the analogy is for the edge at the micro-level.