Every project I tested (mid- to large-sized) had some flaky tests caused by relying on the default row order. In my evaluation of 10 popular PG-based projects, most of them (6 or 7, although its hard to say for sure before sending patches and getting feedback) had at least one application-level bug related to this assumption. This probably isnt a very representative sample, but it at least shows that this is not a purely theoretical issue