If the reputation score is actual reputation, it seems like having a high reputation would be enough to prove you are human. Why do I need to keep proving it? I could see captcha appearing if my behavior became erratic (maybe my account was taken over).
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These spring to mind to me:
Some reductions in CAPTCHA throttle thresholds, if you have > 10k rep:
After successfully completing one captcha, we now suppress captcha for 5 minutes on your account.
Because every user is equally susceptible to having their accounts taken over (the security on every account is identical.) Furthermore, the higher rep users have more power, and therefore their accounts are more desirable to take over.
The more power you have and the more power you use it, the more often you'll get CAPTHA'd. This is the burden of responsibility.