To interpret this research as reason for crippling web or browsers would be a giant mistake. Crippling browsers will only work against users, who will be then forced into installing apps by companies.
Two popular shopping companies in India exactly did this, they completely abandoned their websites and went native app only. This combined with large set of permission requested by apps lead to worse experience in terms of privacy for consumers. As the announcement for Instant Apps at Google I/O demonstrate, web as an open platform is in peril and its demise will be only hastened by blindly adopting these types of recommendations.
Essentially web as open platform will be destroyed in the name of perfect privacy. Only to be replaced by inescapable walled gardens. Rather consider that web allows a motivated user to employ evasion tactics, while still offering usability to those who are not interested in privacy. While with native apps where Apple needs a credit card on file to install, offer no such opportunity.
I am happy that Arvind (author of the paper) in another comment recommends a similar approach:
""" Personally I think there are so many of these APIs that for the browser to try to prevent the ability to fingerprint is putting the genie back in the bottle. But there is one powerful step browsers can take: put stronger privacy protections into private browsing mode, even at the expense of some functionality. Firefox has taken steps in this direction https://blog.mozilla.org/blog/2015/11/03/firefox-now-offers-.... Traditionally all browsers viewed private browsing mode as protecting against local adversaries and not trackers / network adversaries, and in my opinion this was a mistake. """