The correct approach might just be the opposite of whatever you and your team's predilection is. In your case, you're saying that the teams you work with are using inline functions instead of following a restricted framework, in part because they're using languages that encourage them to just slap a bunch of nested code in instead of writing out the extra boilerplate.
Well, they probably already know to be careful about module design -- so if you encourage them to inline less code, odds are pretty good you won't suddenly wake up in the morning with a codebase with a hundred classes and a bunch of obscure private/public methods named `setupEntityExtractorForCollisionPart3`.
On the other hand, if your team is coming from a Java background and half of them are starting from the position that lambdas are just witchcraft, then it's probably not a bad idea to get them over that fear.
In a setting where everyone is inlining most of their code, probably the tests that are coming out are all integration tests, so... yeah, bias towards creating units so you can unit test. In the opposite situation, I'm actually just trying to get people to stop testing private methods and leaking implementation details into their tests. So I would love if people were testing with a little less granularity.
I know that my initial reaction to you listing off the problems you've run into with people building anonymous functions that couldn't be refactored was just, "yeah, but why the heck would anyone make that mistake? How hard is it to organize the variables in one function?" So I assume that other people might listen to my complaints about improper code reuse and think, "yeah, but why the heck would anyone ever just reuse a method in a class without checking the documentation first?" So my takeaway from that is, "different people struggle with different things."