The real pivot here is pivoting from free to paid. The medium isn't an inherent shift in the business model.
Separately it looks like this argument carries more water when talking about digital-only/communication products? Because when considering apps/services such as Uber, HotelTonight and Cherry (I hate picking exceptions) that provide an offline product or service, mobile first seems to have worked just fine. Perhaps the true underlying argument is that mobile first works best when the LTV of your customer is massive.
That said, mobile-first companies are certainly unchartered waters compared to their traditional web brethren. I think they're a bit ahead of their time.
One distressing thing I can see happening: traditional web going the way of the newspaper industry. We're already seeing it with Google. They took a hit in this past quarter's earning's report because their traffic skyrocketed via mobile, but advertisers wouldn't pay the same CPM they were paying on the traditional web.
Sound familiar? Newspapers hit the same dilemma. They went from getting easy $30k tickets for single-run full-page ads to $3k/month online ads (to $300/month mobile-only ads).
Of course, this is a pure advertising model, which is separate from the OP. So... I'll stop here :)