Even if you pay for a subscription to The Economist, you're still going to see ads, both on their website and in their apps. Even though I'm a subscriber and logged in, Ublock Origin is showing over 100 blocked requests on an article I just pulled up there, some of them coming from the same third party ad networks everyone else uses. And my $1 a week subscription only buys me access to three articles a week.
So while, as the OP points out, The Economist's Tom Standage [1] believes that ad revenue isn't a futureproof business model, they still appear to be heavily reliant on it.
I don't know anything about the Economist's overhead, but the reason subscribers are still subjected to ads is very likely that subscription fees come nowhere near covering their costs. The truism in newspaper publishing is that subscriptions don't even cover the cost of printing and delivering the paper to a subscriber.
Subscription-only business models have historically been tough.
A lot of people ask "why can't all advertising be like The Deck," but the trouble there is that The Deck probably doesn't bring in enough revenue for publishers to operate a large newsroom [2]
Personally (not speaking for my employers) I like Brave browser's idea, but they're already facing legal threats. And while they're promising publishers 70 percent of their ad revenue, but even if that's a larger percentage I don't know if that will work out to more than publishers get through the third party networks they use now.
[1] http://www.niemanlab.org/2015/04/the-economists-tom-standage...
[2] https://www.quora.com/How-much-do-content-producers-who-are-...