What prevents aircraft with a tailcone APU from using tail-mounted airbrakes?
The airlines prevent them or: the airlines won't buy them if they were offered

The photos you have already show an APU in the tail section (exhaust on the starboard side).

Adding air brakes requires increased structural integrity (weight; money) and additional system connections (weight; money).

When they are of no use, they're simply not added. Why are they of no use?

Well, pure air brakes (as opposed to speed-brakes/spoilers) have 1–2 functions (for jetliners):


Compensating for the lack of thrust reversers
Performing steep approaches when the thrust-to-weight ratio is high (small plane that has too much power). As I noted here: The thrust-to-weight ratio for the RJ100 is 0.28:1, compared to 0.16:1 for the comparable Boeing 717. It's even higher for the smaller RJ's.


Neither affect most jetliners (note that the babybus (A318) can be certified for steep approaches, and it doesn't need such an air brake).

The airlines would rather carry payload (paying load) and not bother paying for maintenance to regularly check and fix a novel item – not all airports are London City: high thrust-to-weight ratio is good for taking off from short runways and performing steep climbs from in-city airports for noise reduction.