Google and Facebook may choose not to, but plenty of others will. Consider the technical challenges of implementing one set of compliance rules in one place, and one set elsewhere. The profit gain from not following GDPR in an area must exceed the cost of maintaining separate rulesets.
LinkedIn's new policy that goes into effect in May appears to grant GDPR-like permissions across all users, for instance, though it does specify that EEA countries may have additional rights under the law. I suspect the majority of companies will end up complying with GDPR globally.
Under a hypothetical US version of the GDPR, Google might be prohibited from sharing that data with non-governmental third parties. But it wouldn't be prohibited from collecting and storing that data, as showing someone their location history (with clear opt-out language) is actually in the legitimate interest of providing better mapping services for that individual. And law enforcement wouldn't be subject to those third-party restrictions.
There are additional laws that could protect citizens against overreach. But something like the GDPR alone would not do the trick.
This is especially dangerous given that there is already overreach in which data on the correlation of travel and behavior with crime, is being used to unlawfully detain people: https://www.npr.org/2017/12/05/568351544/teens-arrested-on-g... This data would only serve to multiply that problem. It's not an easy problem to solve.
How is remembering where I have been useful to me at all? Hopefully something like a us GDPR would make them excplicitly ask my permission before stalking me.
LinkedIn's new policy that goes into effect in May appears to grant GDPR-like permissions across all users, for instance, though it does specify that EEA countries may have additional rights under the law. I suspect the majority of companies will end up complying with GDPR globally.