Yes pointing a directional mic introduces a whole new set of mechanical challenges.
Maybe you could build an irregular grid of omnidirectional microphones and use signal processing to direct the beam digitally (similar to radio beam-forming). Now you’ll need more processing horsepower to do FFTs to do phase shifts. Although if you assume the bird calls only occupy discrete frequencies you might be able to save some computation by just computing those.
Perhaps a machine learning model could be trained that does all of this for you. Then you get the benefit of hardware acceleration. Some ML chips can handle DSP tasks.
The quality of the single-source classifier is the obvious scientific bottleneck, though; improve it, and everything else will work better. (We've also got plenty* of existing training data for this case.) So that's where we've been focusing most of the energy.
* - depending on species, of course. See also: xeno-canto.org
This is actually the 'real' research motivation behind the bird classification work: Slap a microphone to the side of a tree, pick it up in a month, and get some accurate picture of what species have been in the area.
Birds are relatively easy to observe, thanks to their vocalizations, which makes them an indicator species. We have a good idea what many species eat, so they end up telling you quite a lot about the surrounding ecosystem.
However, it turns out that the 'soundscape problem' where the microphone is just attached to a tree is a bit more difficult than identifying foreground birds only, using a device that can be pointed in the relevant direction by the user.
We've been encouraging further work on the soundscape problem by hosting the BirdCLEF and Kaggle competitions, and have been seeing steady progress. Improvements in the 'hard' soundscape problem have been driving improvements in the 'consumer' identification algorithms.
https://www.kaggle.com/c/birdclef-2021/overview
[source: I've been working with the BirdNet folks on and off for the last few years, and co-host the Kaggle competitions.]