The "penny press" -- starting in the 1830s -- offered low-cost newspapers, basically at a loss, which were then subsidized with advertising. (See: https://en.wikipedia.org/wiki/Penny_press) A similar business model was then used for most newspapers, radio, network television stations, national magazines, cable news/TV subscriptions and on, and on. At each stage, the level of demographic and geographic targeting became more sophisticated. The modern web-based media is basically the logical conclusion of this two-century evolution.
What's more, profitable subscriptions for media are at an all-time high. The issue is that the spoils go to only a few winners, like Amazon, Netflix, SirusXM, Spotify, Comcast/TimeWarner, etc. A real issue is that people are more willing to pay subscriptions for music & entertainment than for news & analysis. But that's changing.
NYTimes, WaPo, WSJ have large-scale digital subscriber programs, and mid-market publishers are following suit. But, it's never going to have as much scale as ad/attention-based monetization.
I tend to agree with the sentiment embedded in your statement -- that if media are subscriber-based, they tend to be better aligned with those readers. But people are definitely accustomed to free on the web.
I recommend you check out "The Attention Merchants" to learn a bit about how news and information has been paid for over time. You shouldn't blame measurement; you should, if anything, blame the media industry's unit economics: http://amzn.to/2osFiNz
Any recommendations written by a historian instead of the author?