As someone who has actually issued visas, I have no idea what you mean by "bureaucratic nightmare." When vistors are issued their visas overseas to enter the US, they understand the length of time the visa is valid for. They must prove that they have a valid reason to extend their stay in the US beyond the authorized period. This country is no different than any other when it comes to the extension of a visa. Can you identify any other country that makes it easier and faster?
In any case, I don’t know why we should care what other countries do, unless they find something that works really well and might work here
Then you don't understand the concept of reciprocity. American citizens deserve equal treatment from other countries, i.e., the same treatment we provide their citizens. To demand less puts our citizens at risk in many ways.
Doesn’t seem to work that way, or, judging from way Mexico treats gringo lawbreakers, a lot of illegal aliens pray for deportation if we “reciprocated”...
In general, I’d expect the US to behave better than the “lesser breeds without the law.”