Using "as in/ like in"

Question

I was watching a video and the guy in the video said this :

"... All the methods I have talked about in the past are correct but there is an alternative path like many things in training" (he is talking about different exercise methods.)

I wonder why using "like many things in" above sounds idiomatic but using "like the case in" in the sentence below sounds unidiomatic ?

1- As is the case in a plethora of English-language papers, the writer chose this extremely common construction. (This was written by a native speaker.)

1a- Like the case in a plethora of English-language papers, the writer chose this extremely common construction. (I was told that this was not at all idiomatic.)

Answer 1

like is for a comparison.

• He is like my brother. [[He resembles my brother as regards his behavior]].

as in as is the case is merely introducing an example of an actual case or other thing. There is no comparison.

• As is true for most French people, Americans like cheese.

like many things in training = similar to other things in training. That is comparing methods to other things one encounters in training.

Now, the trick is to realize that in everyday speech, people will often use like instead of **as.**

• Like many French people, Americans like cheese. [comparison] FOR:
• As with many French people, Americans like cheese. [What applies to French people also applies to Americans.]

It is a question of language register. (formal versus informal)