They have attempted to make this but you have to be rather specific to trigger local results. “Chinese takeaway” will not trigger it for instance but “Chinese takeaway near me” will.

Improving this is hard but a possibility I see would be to have certain categories of search default to region-local (as in: country, general region) or location-specifc (town, borough).
Searches on the topic of shopping, taxes, bureaucracy etc. should automatically make results local.
Searches on the topic of restaurants, shops, leasure, transport etc. should be location-specific.

Determining these topics would be the hard part though; especially given that it’d have to happen in multiple languages.