Google isn't providing a service to you, they are providing a service to the site that uses the captcha. And they haven't put any roadblocks, the site did - by installing a captcha.
You should complain to the site that decided to offload their captcha costs to you.
I don't see why they would. If some delivery service had an expensive pay-on-delivery model, and some ecommerce site decided to use it, but didn't tell you (the buyer) that they did, and so you got a surprising shipping bill on receiving the product, would you blame the delivery service?
Your relationship is with the site, and so it should be their responsibility to inform you of the "bill" you'll have to pay to Google for using the site's captcha-protected services.
The analogy doesn't hold. For this argument to be valid, we'd have to pretend that dark patterns don't exist.
And, Google is definitely employing a dark pattern here. This is designed to be a stealth tax, to go largely unnoticed by anyone, including the site operator.
Even Google's selling of the product doesn't make clear that users will be doing additional work; instead suggesting that saving the world will be a by-product of a normal captcha process. [0]
You should complain to the site that decided to offload their captcha costs to you.