For many websites, ad revenue is the biggest source of revenue. And if it's not it is usually because they have a source of revenue through affiliate income, info-product income, or they're just starting. So that's why they don't want you to have AdBlock on.
To answer your question about if the website gets money from you merely having the ads on, rather then just clicking it and the answer would be yes.
For starter websites for every 1000 pageviews of the ads, you get around $1. For websites with more traffic, it is more like $20 for every 1000 pageviews.
But one click regardless if it is a starter website or a website with more traffic can range anywhere from $0.20-$3 per click sometimes even higher for some clicks.
Then there are also websites that have video ads and moving ads literally everywhere so they get more views on the ads. Ads are necessary to keep a website running, but excessive ad placement can be really bad for a website because a lot of people will just leave the website after that which will increase there bounce rate (if a user leaves/jumps off of a website quickly) which is bad for SEO (Search Engine Optimization - how much google ranks them).
Also, some ads that you see on a website might not be from a place like Google AdSense, ezoic, mediavine, or something like that. But it can actually be an ad placed by the owner of the website that only gets revenue if you click on the ad and purchase whatever is in the ad. As in the ad is an affiliate link. And if they are using these types of ads, which most website owners don't often do. They wouldn't get revenue from you merely having them on. A good example of this would be Investopedia that often has this type of ad...
In this ad, they would only get revenue if you clicked the ad and opened an account through the link. Sometimes these links also have cookies, which means if you pressed the link today and opened an account tomorrow there's a big chance they still got revenue for that.