This phenomenon back home in the States varies. The lower the class of the clientele, public, or local user base, the less privacy there will be. There is no practical or benevolent utility to the wide spaces except to deny privacy in the bathroom. The ADA has no standards for clearance under a door to a toilet, although the space under a door is generally just enough to see feet in non-security-theater countries.
Doors with wide hinges and that "hang away" from the frame are actually more expensive and difficult to maintain, and are sold featuring their viewable apertures on each side (hinge- and latch-side pillaster clearances). These are often sold internationally as 'US style'. Americans (especially the more conservative or deprived segments of the herd) are a fearful, often oppressive lot, as most well know. Nothing illustrates this more than the small touches added to everything that bespeak their fears of 'someone might get away with something I disapprove of'.
As an architect, I can tell you that the only purposes in these gaps is to discourage comfort, satisfy resentment at the requirement to provide minimum facilities on the part of public accomodation locale business operators and conservative lawmakers, enable dehumanization and humiliate the lower classes. It is the same reason that US transit stops are often not weather-safe and have discomfort in mind (under the aegis of preventing homeless 'camping', and thereby non-participation in rent regimes). It is the same reasoning underlying the use of inordinate amounts of privacy invasion for basic interaction with any institution at the middle class level or below: frivolous and pointless oppressiveness and an ever-present precarity to keep people in line.
If one goes to or frequents reservation-limited municipal golf courses; country clubs; higher-tier restaurants, hotels, their associated cocktail lounges; and facilities in more homogeneous areas, these little touches disappear. A public park in the same city will have no doors on the stalls in the 'poor' part of town, not to mention likely prison-style fixtures for toilet paper (if any is on offer) and will generally lack sanitary supplies. However, in the richer part of town, a similar park (in addition to newer, better children's play equipment and sports facilities, as well as maintained landscaping), will have full privacy in well-lit, meticulously maintained restrooms with modern equipment and special touches (clean baby changing stations with filled wipe dispensers, heated water as well as the standard cold, and paper towels and toilet paper, present and of good quality).
Any other offers of explanation, really, are delusions. Americans blend classism with bitter, petty security-theater antics to keep the labor class on their knees.