That would be extremely annoying to anyone that uses public wifi, or any sort of VPN/TOR.
It's already an almost impossible task to do google captcha's on a tor browser, let alone if you have to do it multiple times for each post that you make.
That's why my suggestion was for only newbies and Jr. Members. I do not think a legit newbie/Jr. Member posts that much. Twice or thrice a day? A legit one basically will spend more time on reading then posting IMO. We can be more flexible by reducing the captcha requirement only for Newbies, if we want.
We already have a restriction for newbies, which is can not posting image. We can easily add the capcha requirement for them as well. Both can be lifted if they buy copper membership.