When is Data Driven Decision Making applicable?

Agile companies usually declare "Data Driven Decision Making" as a fundamental principle, because data forms the basis for empiricism.
The standard Retrospective format lists "Gather data" as one of the key stages. But when is it actually a good idea to start gathering data - and when do we stop gathering data?

To understand why we would even gather data, let us start with the problem. Basically, we want to gather data in order to help define the problem we observe and how we are going to solve it. Gathering data without a problem that needs to be solved is waste.

Here are a few types of problems you might be facing:

We don't (really) have a problem with that

Well, then ... work on something that is a problem. Easy.

We already know the root cause and solution

Well, then ... Go Fix it! Easy.

We know the root cause, but no solution

We need to devise an experiment that may bring us one step closer to the solution. After weeding out alternatives, we definitely need to gather data of some sort to help us decide if this experiment can be successful and - after trying it out - whether it actually helped.

We know the root cause, but it's outside our sphere of control

If you can't control it, but you can influence it, the best strategy may be to "make it the problem of someone who can solve it". Find a problem owner who can actually help.
There is not much value in gathering more data, unless that data is required to win a problem owner.

We know the root cause, but it's outside our sphere of influence

This happens, for example, when the problem is caused by a new law passed by the government. You have two choices here: Either, adapt to the new situation or work around. Gathering data will not help you solve the problem, because no solution you devise will be realistic.
However, you might want to collect data which helps you re-define the problem "given the existing external constraints".

We don't know the root cause, or: We don't understand our problem

This is the obvious use case for "Gather data" - go find the root cause, and learn which data can help you do that.

Summary

Data Driven Decision Making has it's uses. However, it is also limited in use. Gathering the wrong or unnecessary data is waste and should be avoided. Which data is "wrong or unnecessary" depends on the problem you are facing.
Therefore, a clear understanding of your problem is essential before actually spending time with data acquisition.