I don't think this is inherently the issue. News sites could aggregate charges and bill you at the end of the month.
I think the bigger issues is that if I see an article presented to me as shared on social media or in search results I assume it is free access. I click in, and if they ask for payment, it's a turnoff since I thought it was going to be free. Also, I don't like how credit card information can be continuously used by the organization.
I want to be able to hand an authorization for a single one-time payment to any organization and not an authorization to charge however much they want, whenever they want.
That goes for hotels too. I want to be able to say "Here's my credit card" [but I don't authorize more than $130/day].