The point is that scraping is already inherently cost-intensive so a small additional cost from having to solve a challenge is not going to make a dent in the equation. It doesn't matter what server is doing what for that.
In reality you can do maybe a 1/10000th of that before the latency hit to real users becomes unacceptable.
And then, the cost is not per page. The cost is per cookie. Even if the cookie is rate-limited, you could easily use it for 1000 downloads.
Those two errors are multiplicative, so your numbers are probably off by about 7 orders of magnitudes. The cost of the PoW is not going to be $2B, but about $200.