several newspapers are offering to deliver copies, which they don't normally do, probably fearing just what you suggest - that people who have turned to online news sources may not come back.
The market for news is distorted by the BBC, whose website is free (ie paid for out of the licence fee - and by advertising abroad). So the British in particular seem to feel entitled to free news. The Mail is doing fine, though the website has a lot more celeb/cellulite stuff than the papers. The Guardian is keeping its head above water by offering everything free online but inviting readers to subscribe anyway, which many do. The FT is doing well with its online firewall, since people will pay money to find out how to make money. Nobody knows how the Murdoch media are doing behind their firewall. The Telegraph is struggling. Local papers have been dying for years, which is a shame.
This is long-term and to do with the internet rather than Covid 19. But like most industries, media are suffering under the lockdown. Even with paywalls, media websites rely a lot on advertising but advertisers are spending less.