I guess I'm *kinda* confused by the question just based on how you've worded it - are you asking if you should put a 22 3/4" cabinet over your range with the hood mounted underneath?

Do you have a soffit above all this? Do you have a specific need for the cabinets above?

Honestly I think 24" between cooktop and hood is going to drive you nuts, I'd go a little higher like you're thinking.

Here is a link that might be useful: GW Hood height discussion

I'm with Swen - 24" is mighty low.

In my city, the code requirement is for the height of the cabinet above the range - not the hood itself. I think it's 30". I asked my cabinetmaker to go as low as code allowed, because I'm 5'4", and wanted to be able to reach into that cabinet. But then I found a hood that's only 5-1/2" tall, to maximize the space below.

I think Boops is saying that has 18 inches between her countertops and 36 inch flanking cabinets. and can raise her hood to 26 3/4 inches above the counter if she shortens her above hood cabinet to 20 inches (and still align with the 36 inch cabinets alongside the hood).
Comfort in height depends on depth of your hood and height of your cooks.Sufficient ventilation depends on your cfm's as well as depth and width.
I mocked mine up over the sink with some wood supports and beams and decided that 30.5 inches was the right distance for us with a 24 inch deep hood and 600 CFM's.
If you have the ventilation power and capture size you may want to raise your hood even higher if your hood is deep to avoid a "head banger".

Thanks for the replies. Mocked up a cardboard hood- thinking the 24in is not high enough. But the 30 is too high. My solution? Split the difference and go with26 high for hood from cooktop, which makes the cabinet height 20 3/4. One more thing off the list.