And that advice is simply wrong. It's simply not possible for any team to reasonably assess the pros and cons of a given software development methodology - with the possible exception of the one they're already using - in a week.

Suggesting a team 'try a methodology for a week' is inviting a train-wreck.

Good to know you're the benchmark for productivity in the industry.

My own experience - across multiple teams, multiple organisations, multiple languages and frameworks - is that it can take weeks to evaluate even relatively slight changes to existing methodologies.

Let's say the OP decides to adopt Extreme Programming.

How long would you say that a team with zero experience in that methodology would take to get to the point where they're practising it well enough to perform a useful evaluation of the consequences?

Less time than it would take for you to realize that our experiences form only our perceptions, not universal law.