Not even remotely absurd. Where is the data your scraper consuming coming from? It's almost always served from some sort of data repository (SQL or otherwise). That data costs far more per MB to serve up quickly than JS/CSS/images.
Suppose, for example, you host a blogging platform that has one very popular user. Most accounts on your site don't get a ton of visitors, and that one very popular user's post are all stored in cache.
Then along comes a scraper. He thinks, "Hey, this site is serving up a million page impressions a day. It can definitely handle me scraping the site".
But when he runs the scraper, he fills up the cache with a ton of data that it doesn't need, causing cache evictions and general performance degradation for everyone else.