I can speak with some knowledge of a not-insignificant B2C company -- not my current gig -- that went down this exact same route some years ago.
Swore off mobile web in favor of pushing people to the app, because app conversions were much higher.
A satellite office broke away from the fold and implemented a responsive mobile site, immediately increasing their bottom-line revenue by 30%... and that's before doing any sort of conversion optimization.
The main office followed suit shortly thereafter... with a new head of engineering.
Native apps are no easier or harder to build than web apps. Equivalent level of difficulty in my experience, with apps being slightly harder because end-to-end testing needs to be done almost completely manually, and because the release cycle is partially outside of your control.
But for most businesses, you really, really do not want to neglect the mobile web.
Yes, conversion for in-app users is broadly higher across the board. But that's not because conversions suddenly spike when people use an app. Rather, your most dedicated users -- the ones most likely to convert -- are the ones that will install an app.
For the rest of us, if it's "app or bust", we will pick "bust".
As a consumer, I deal on an annual basis with probably over a hundred different companies. I do not want an app for each of those companies. And if you force me to download an app from the get-go, I will go to your competition.