Just my opinion. I like the idea of being able to see/clean under the base. I am always reticent to create a convenient fort for the little critters to set up shop. As far as cleaning under there, a simple round long feather duster should do the job. (Not that I am a cleaning junkie) Others could probably give you some better solutions there. I also like what the cutting out did for the style. I think with the other aesthetics of this piece, with one simple cut out on the bottom, it went from looking a little bit like an industrial planer, to a finely designed furniture piece. I totally agree with you when you said, "It was too bold, and the cut made a world of difference".
Pertaining to the bottom having a sharp edge on it, and creating a danger for the toes, I am at a loss for an ideal solution. The sharp edges actually add to the aesthetics. Naturally you think, round the edges, and cut the sharp tips a little rounder on each side of the bottom. The problem is that I like the look of the sharp edges and tips that echo the crisp lines of the piece. That's a tough one. Currently my bathrooms have old vanities and they have the toe kick, enclosed bottoms, as well as the kitchen cabinets, which have the same. I can see how that would solve a lot of problems.
As far as the offset with the sink basin, my initial thinking is that with the sink in the middle, you have the best chance of avoiding the splash factor hitting the floor, and/or an adjoining wall. I'd rather see it stay contained on the easy to clean up counter top area. Bending over to clean up any splashing on the floor is great if you're looking to practice yoga while cleaning.
Additionally, if you decide to keep the sharp tips on the bottom, the basin in the center will help increase the likelihood that a foot will make it under the softer rounded center, rather than in the offset area, where the sharp tips are.
I'm planning on creating bathroom vanities for 2 bathrooms, so this post is giving me a lot of room for thought. I too like the fluting, and it looks like the grain pattern in the wood will look great if you are planning on naturally finishing it. Nice looking piece.