There are two simple factors with opposing relationships:
- Work clearance
- Vacuum effectiveness
The manufacturer wants the hood as close as possible so it's more effective at scavenging gases, but they know you need clearance to move and cook. That's really it. Fire danger isn't much of a factor until the hood is mere inches from the burners, and who's going to do that?
Regarding reduced effectiveness at greater heights, I'd expect an accelerating reduction in scavenging with height. If you think of your hood's area as a portion of the surface of a sphere centered on the stove top, the further away you go the smaller that is as a portion of the sphere's surface1. It shrinks substantially as the effect of local breezes increases. (Simply walking by pulls a lot of the fumes along with you, out of reach of the hood2.)
Therefore, that 30" number isn't "concrete", but it's notice that you lose a lot of exhaust function if you go beyond it. There's not much science to be applied due to the great potential for variation in local conditions3. Any claims to numbers would necessarily assume averages from a large range of values.
1 It's an oversimplification for sure, but let's take a look using the hood's box area (which may not even be appropriate; the duct opening might be a better reference). The area of a sphere at 24" radius is 1809.6 in2. The portion of a range hood of say 20"x30" is 3.31%. If you move out to 30" it drops to 2.12%. That's a proportion reduction of ~36%. Move out to 36" and you're down to 1.47%, or another 30.6% smaller and less than half what it was at 24". The reduction in effectiveness as a result is compounded by dynamic air movement in the room and time.
2 Beyond its event horizon, if you like.
3 HVAC type and location, room size and shape, window usage and location, door usage and location, ceiling height, human activity, etc., etc. It quickly becomes a study in chaos theory akin to predicting the weather.