Open source makes it easy for the cat in the cat mouse game, right?
There's no real cat & mouse game here (yet*) - sites don't do anything to mitigate this. Sites deliberately make their content available to robots to gain SEO traction: they're left with the choice of allowing this kind of bypass or hurting their own SEO.
* I say "yet" because there could conceivably be ways to mitigate this, but afaik most would involve individual deals/contracts between every search engine & every subscription website - Google's monopoly simplifies this somewhat, but there's not much of an incentive from Google's perpsective to facilitate this at any scale.