So your solution is to deploy a black box that can be worked around with a basic lookup table for a single field?
CAPTCHAs were never meant to work 100% of the time in all situations, or be the only security solution. They're meant to block lazy spammers and low-level attacks, but anyone with enough interest and resources can work around any CAPTCHA. This is certainly becoming cheaper and more accessible with the proliferation of "AI", but it doesn't mean that CAPTCHAs are inherently useless. They're part of a perpetual cat and mouse game.
Like LLMs, they rely on probabilities that certain signals may indicate suspicious behavior. Sophisticated ones like Turnstile analyze a lot of data, likely using LLMs to detect pseudorandom keyboard input as well, so they would be far more effective than your bespoke solution. They're not perfect, and can have false positives, but this is unfortunately the price everyone has to pay for services to be available to legitimate users on the modern internet.
I do share a concern that these services are given a lot of sensitive data which could potentially be abused for tracking users, advertising, etc., but there are OSS alternatives you can self-host that mitigate this.