If you are using TOR, and not accepting cookies, they are going to have no way of knowing that you are the same user who just solved the CAPTCHA. Every request is going to appear to be from a new user.
If you do everything you can to prevent google from knowing who you are, don't be surprised when they behave like they don't know who you are.
A botnet doesn't need Tor in the first place. And you can limit the use of a single captcha solution. It's not much different from the problem of a legitimate google account being borrowed by a bot.
If you do everything you can to prevent google from knowing who you are, don't be surprised when they behave like they don't know who you are.