>I’m a little confused by what there is to investigate at all.

One of the most important aspects of taking safety seriously is that you do not just investigate things which had an impact, but that you proactively investigate near misses (as was the case here) and even potential incidents.

A plane with 6 minutes of fuel left is always a risk to every person on board and potentially others if an emergency landing becomes the only option.

Indeed that is the definition of a "aviation incident" where there was a risk of injury or damage. If there is actual injury or damage it becomes an "accident".

The investigations into incidents aren't usually particularly long or noteworthy and often the corrective action will be to brief X on dangers of Y, or some manner of bulletin distributed to operators.