Functions should be small and do one thing […] you end up with a slew of tiny functions scattered around your codebase (or a single file), and you are forced to piece together the behaviour they exhibit when called together
I believe you have a wrong idea of what “one thing” is. This comes together with “functions should not mix levels of abstraction” (cited from the first blog entry you referenced). In a very low-level library, “one thing” may be sending an IP packet over a network interface. Higher up, “one thing” may be establishing a database connection. Even higher up, “one thing” may be querying a list of users from the database, and higher up yet again is responding to the GET /users http request. All of these functions do ‘one thing’, but they rely on calls to a few methods that are further down on the abstraction scheme.
By allowing each function to do ‘one thing’, you decompose the huge problem that responding to an HTTP request actually is into more manageable chunks. When you figure out what a function does, it’s way easier to see that the function connectToDb will not be responsible for why all users are suddenly called "Bob". You’ll look into the http handler first, and if that’s not responsible, into getUsersFromDb, and then check what sendQuery does. If all methods truly do one thing, you’ll be certain that checkAuthorization will not be related to the problem.
Tell me if I just didn’t get the point you were trying to make.
Edit: I just read
Martin says that functions should not be large enough to hold nested control structures (conditionals and loops); equivalently, they should not be indented to more than two levels. He says blocks should be one line long, consisting probably of a single function call. […] Most bizarrely, Martin asserts that an ideal function is two to four lines of code long.
If that’s the standard of “doing one thing”, then I agree with you. This is stupid.