You don't need the Internet for ambiguity to occur, you only need to go international. It may be because you travel, or work with foreigners, or handle mail/packages to/from abroad. Or use any kind of software, because unless you live in the US, almost all software you use is made by foreigners in a foreign country.

In a globalized economy, local date formats are just one of those annoyances that serve no benefit, cause everyone unnecessary hassle, occasionally causes expensive errors, and that should have long ago been replaced with an international standard.