Machine learning researchers publish most of their work on Arxiv first (and often, only), so peer review will not stop wild claims from being publicised- and overhyped. The popular press helps with that as do blogs and youtube accounts that present the latest splashy paper for the lay audience (without, of course, any attempt at critical analysis).
As to traditional publications in the field, these have often been criticised for their preference for work reporting high performance. In fact that's pretty much a requirement for publication in the most prestigious machine learning conferences and journals, to show improved performance against some previous work. This strongly motivates researchers to focus on one-off solutions to narrow problems, so that they can typeset one of those classic comparison tables with the best results highlighted, and claim a new record in some benchmark.
This has now become the norm and it's difficult to see how it is going to change any time soon. Most probably the field will need to go through a serious crisis (an AI winter or something of that magnitude) before things seriously change.