APKWS interceptor is about 35K USD and works much better than drone-based interceptors. The problem is to scale the production, training and deployment. Another problem is detection. One needs wast multilayered system that US military missed to build as big stationary radars are very hard to defend.
Air-launched interceptors like this have the problem on relying on a super-expensive manned carrier (fighter or helicopter).
The intercept cost is now not only the cost of the interceptor, but also the cost of the flying hours of the launching platform, and the risk of losing the launching platform.
If you equip even some of your Shaheds with AA missiles (cheap manpads with autonomous IR target acquisition and guidance), like is already happening in Ukraine, the feasibility of APKWS becomes problematic. The technology is developing fast these days.
APKWS launching from air is a stop-gap measure in any case. The detection range for Shahed-type drones is tenths of kilometers, not hundreds, like with fighter jets or big missiles. One cannot have that many fighter jets in the air all the time even without the threat of manpads.
But ground-based platforms work just fine and cheap enough to scale up the deployment to cover the big area.
The big advantage of APKWS over interceptor drones is the rocket engine, they are much faster and can catch Shaheds within much bigger radius or within much smaller timeframe than interceptor drones.
First, if I understand correctly, APKWS is laser guided (one of the reasons it is relatively cheap is cheap simple guidance), it needs the carrier to designate the target.
Second, it is rather short range, and that range is helped significantly by the speed and altitude of the launching platform. Launching from the ground upwards would significantly reduce its range, which is anyway just a few km.
Due to the short range, you will need a densely distributed significant numbers of them, and still be in danger of saturation attack (the attacker can saturate one route, you have to be ready for all possible routes). Having a carrier platform allows the missiles to be quickly brought where they are needed, so overall you need much less of them (still too much, as having enough carriers in air imposes limits as well).
You can have longer-range ground missiles, but then the costs rise. Also, I am not sure how feasible/robust is to laser designate air targets from the ground. I suspect it does not work over longer distances, i.e. you need a more sophisticated and costly guidance system/sensor suite on the missile.
The beauty of an anti-drone drone is that you have a much more robust human-assisted guidance, for cheap (camera and communication link). With advances to AI, even that human and communication link are becoming obsolete...
With rocket propelled missile you have much faster closing speed, and quite limited energy budget - essentially you have to make a correct decision fast and precisely, otherwise the missile is wasted. With a drone, everything is slower and easier to correct.
The latest APKWS is IR guided and works in fire and forget mode that works nicely from the ground. And then drone interceptor struggles with Russians Shaheds with jet engines.
On the other hand the latest development with drone interceptors is rocket booster to quickly bring in within Shahed. So I guess there would be a convergence between APKWS and interceptor drones.
IR guided fire and forget is fine, but undoubtedly quite a bit costlier than the basic laser-guided one. If you want to use it against jet engined Shaheds while launching from the ground, you definitely need larger rocket motor, i.e. costlier interceptors. But that might be fine, the jet engined Shaheds are not as cheap as the basic ones anyway.
Actually, I am surprised they still use the Shahed platform for the jet engined drones. A Reaper-like platform with high aspect ratio wings would be much more aerodynamically efficient, allowing longer range/loiter time/larger payload. It is definitely more expensive airframe, but that jet engine might be the main cost factor anyway.
Re: IR seeker against plain Shaheds: does the basic weedwhacker Shahed have enough IR signature? (More precisely: does it have it if you did some basic precautions - cover the engine, some mixing of the ambient air with the exhaust.) The power level of that engine (= the whole source of IR energy) is quite low...
Shahed shape is dictated by the need to sustain very high G and aerodynamic forces during the launch from a truck which in turn allows for a very fast deployment. Anything more aerodynamic will imply stronger, more expensive frame and less payload.
Shahed has sufficiently bright IR that even a basic seeker works. To keep the cost low no efforts were applied to minimize the signature.
It is fascinating how well designed Shahed was for its intended purpose of being the cheapest mass-produced platform that would saturate any advanced air defenses while hard to track launch site. However, with appearance of cheap mass-produced counter-measures it may no longer be optimal.
If Iran launched 10000 Shaheds towards Isreal, you can be sure quite a few would get by.
Maybe Ukrainian drone interceptors can be made cheap enough to be good enough against massed Shaheds.
We are still early in the new paradigm, there will be significant developments.