> The core of functional programming is about avoiding mutable states, not much about anonymous functions or passing functions as data.

I disagree since any paradigm can be done either with or without mutable state. So it is not something that defines functional programming.

In any case you can also use immutable data types with python anyway.

The main annoyance with python is in my opinion your last point: The lambda syntax is too limited. So it is necessary to define lots of nested small functions instead.

Also python syntax is not as nice in chaining function calls over multiple lines.