The theory of "overkill" by prehistoric man as a likely explanation for the extinctions was suggested by Paul Martin as long ago as 1967. It is still not generally accepted and writers on evolution (being salaried academics with careers to think of) tend to skirt round the subject with great caution. See Wikipedia articles.

The obstacle to its acceptance is perhaps an idealised perception of "prehistoric man" as an animal in balance with nature and existing in relatively small numbers - a "noble savage". Perhaps this perception contains an element of truth until the appearance of language and tribal organization. But what happened in America happened only about 10,000 years ago. The invaders of America and their Eurasian contemporaries were not primitive - they are likely to have been organized in large tribal groups and they certainly had relatively sophisticated weapons.

One problem remains - how did the elephants and many other large animals survive in Africa and to a lesser extent in southern Asia?