there is absolutely no reason that they cant do both at the same time, there is a mental short circuit going on when people think paying for a website means no ads. Its never meant that in pretty much any other media.
Yes there is a reason, users often don't expect to pay for services that show ads, and users who pay for services often don't expect to see ads. That's why most popular online services don't mix the two, eg. Facebook, Spotify, YouTube, Netflix, Crunchyroll, Google, etc.
"mental short circuit" better describes your argument that jumps from "it's possible to both show ads and charge user fees" to "they always will".