Nonsense.
If you make the content of your site freely available with the knowledge that users can access your site in a way that circumvents your business model you've signed up for a business model that isn't dependable.
This is no different than a street musician wanting money from people that stop to listen to the music they play. Maybe the listener, having heard the music, determines it's not of any monetary value. Are they obligated to pay anyway? No, and the street musician knows this. They understand that only a certain percentage of people that stop to listen will actually pay anything. It's true, too, that maybe someone will listen to the music and be unable to pay. Should they block their ears as they walk past because they cannot give what the musician would like to receive for his service? In the case of a screen reader, maybe the user doesn't even know the ads exist.
If the street musician decides his business model isn't supporting him as much as he'd like, maybe he'll stop playing music. And will the public that decided to not pay him anything really care that he doesn't play it anymore? No. They decided it wasn't valuable enough to pay for.
If you feel your content is worth something or you need money to continue providing it, you should charge people for it outright, or make an explicit request for donations. If people find value in your content and are able to, they will pay for it.
It should not be expected that when you put content freely available somewhere, whether it be publishing a blog or playing music in the street that everyone who reads or hears it finds it of equal value or is willing and able to pay for it. You, as that site owner or musician do yourself a disservice if you expect otherwise.