You could, but once you need to turn around and thrust upwards to avoid hitting the ground, you'll need to run the motors HARD, which will make a lot of turbulence right below you, which you then fall into. So you're falling into wind that is already blowing towards the ground, so you need to push it down even faster, and so on.
Ducted fans might help a little, since they can send the turbulence further away faster, but then you have the additional mass of the ducts, and the inefficiency of accelerating the air to higher speeds, since larger slower props are more efficient (but less responsive), to the point that this is possible: https://www.youtube.com/watch?v=emK-qIbuJ-k
I wonder if, for autonomous (or semi autonomous) flight, there's a way to make the drone flip and "power dive" then fly a carefully configured/programmed half-loop at the bottom? Seems there might be scope that way to have an autonomous "reduce altitude as rapidly as possible to 5m" function on a button that'd fly a full power j shape and compensate for the semicircular radius of the "deceleration without flying through your own prop wash" part of the maneuver? Similar (but more complex) to the "flip" and auto land functions on "toy" drones?
(I wonder if the drone people from Ukraine already have this? I suspect it'd make drones even harder to defend against with anti aircraft system designed and optimised to shoot down fighter/bomber planes instead of swarms of inexpensive drones.)