Edward Tufte is highly recommended on the topic.

It's not a hard rule, more encouragement to investigate ways to make the presentation more informative by relating the data to it's context, time etc.

A pie chart is one-dimensional, quantities period.

His book "Envisioning Information" was very influential for me.

I would still argue that a stacked horizontal bar with tick marks or a waterfall chart are often the better solutions. They also make it easier to provide a reference point for the absolute sum of all data points

I think pie charts only work in those cases where it doesn’t really matter how big individual data points are, but where one only wants to give a feel for the relative weight of 2 (max 3) data points. But then: wouldn’t a simple KPI (“55%”) suffice?

Stacked bar charts have the same weakness as pie charts where it is very difficult to tell the relative sizes of the pieces.

I'd argue even 4-5 things can still be ok given they're significantly (enough) different sizes. Recently I needed to show how our online revenue was split between 5 different products and the pie chart worked perfectly.

With favorable numbers pie charts can be readable, but what makes them better than a bar chart?

At least to my brain, showing 'parts of a whole' is easier to intuit in a pie chart than a bar chart. Again, the caveat being there aren't more than 4-5 parts and the sizes are different enough.

That said, I'm now interested in asking around the office to see what others think. Maybe I'm an outlier and should switch to bar charts.

Pie charts shine when there several data points that can be grouped into 2-3 macro groups.

The easiest example is "What is your opinion of ___?" (Strongly Favorable, Somewhat Favorable, Neutral, Somewhat Unfavorable, or Strongly Unfavorable)

At a glance, you can see if the opinions are positive or negative, and then can see if they are polarizing or mostly neutral.

Another example would be the makeup of congress. Democrat, Independent, and Republican for the major groups. Subgroups could be based on percentage of votes the person received from their district. It would show which seats could swing.

Generally agreed. I think 4-5 data points is fine, but the advantage of pie charts is that it's a quick visual representation of what proportion of the 100% can be attributed to the 4-5 segments.

Pie charts fail again once the distribution is very skewed (1 segment = 99% and the other 3 shared 1%). It also fails when the distribution is too even (5 segments 20% each). They shine the most when there is variance, but overall easy to interpret the distribution differences.