The "sponsored by viewers like you" approach (aka Patreon, the NPR pledge drive, etc) solves this problem, but it's rare that anything has an audience big enough to support it.
But hey, one of the benefits of sponsored content is that at least the ads (if that's how the sponsorship works: it usually is in podcasts and video, which are where this is really taking off, moreso than blogs) are entertaining. I skip ads as quickly as possible for the most part. OTOH, I have repeatedly watched an hour-long compilation of ads for SquareSpace taken from the Co-Optional podcast. Which were compiled by popular demand.
So that's a benefit to sponsorship for companies: if you can get me to willingly watch your ads, because they're that good, you've effectively won.