If you look at just the I/O overhead involved for fetching state of joystick, you will see that it involves multiple I/O instructions and other overhead and it's slower than a MOVE.W of Amiga. And you are going through API which doesn't allow you to take over the USB for just joystick.
Nobody wants to poll the joystick at 1kHz. Nobody anywhere in the entire world. Nobody, that is, except for you.
Let's just distil all this down to the basic facts here.
You have not given any evidence, anecdotal or otherwise to demonstrate that any commercial software ever written for the Amiga uses high resolution joyport polling to better capture the user's input.
The single, meaningful example of why polling the joystick at anything like the kHz range makes sense was given not by you, but by me. That example was the cassette tape interface for ZXAM which basically converts the incoming tape audio to a series of pulses on the joyport fire pin.
Your ability to record the joystick at a high rate in no way whatsoever demonstrates that River Raid (your chosen example) does so. Your sole evidence for this was that replaying events captured at a higher rate gave better, more predictable results. That does not tell you
anything about the actual sample rate of the game itself. All it tells you is that you can better reconstruct the original joystick event stream by recording it at a higher rate. This is basic sampling theory: the reconstruction of any signal is better at higher sampling rates. It does not mean that the game is sampling at this rate. For instance, if I sample spectrum audio at 8kHz, replaying it back to the spectrum tends not to work very well. Recording and replaying at 22kHz works very well. We do not infer from this that the spectrum is reading data at 11kHz (the highest frequency you can hope to reconstruct at 22kHz). Far from it, it switches between 1-2 kHz using PWM encoding for bits.
The joystick example is the same. Even if River Raid samples the joystick once per frame only, you will be able to replay a recorded sequence of events more accurately if that recording is at a much higher sample rate than the game is using, simply because your recorded signal more closely resembles the original signal at higher rates and not because the game requires it.
So, you might very well be able to poll your joystick at a faster rate using CIA timing but I'm still waiting for an explanation as to what tangible advantage this gives with respect to human input for a joystick.