The LA Times makes money from subscriptions. How many EU citizens do you think would purchase LA Times subscriptions if the site complied with the GDPR?
If webmasters in Europe stop linking to you, Americans traveling in EU lose your trust, and EU-hosted search engine crawlers figure you don't exist, then you start to have some problems.
A good businessman is able to change its assumptions when the world around him changes. In 1980, it might have made sense to limit your newspaper audience in the area where you lived. In 2010+, due to the Internet, the main cost of a newspaper consists in the work performed by the writer to produce the actual content. When the world around you gives you basically free infrastructure to send those bytes to another continent against a one-time investment of assessing and fixing your site for compliance, you just don't say no.
As an addition to the GP's argument, consider that these days, news stories are meant to be linked to on social media. People have friends and audiences in many places in the world. If someone with parts of their audience in Europe wants to share a news story, will they choose an article on GDPR-blocking site, or on a GDPR-compliant one?
The most important factor is still if your newspaper is any good.