"becoming a doctor is not that important to me" vs. "for me"

Question

A post gives good examples to distinguish "important to" and "important for"

1. "It is important for you to get well" ~ your life will be improved by returning to health
2. "It is important to your family that you get well" ~ they put a high value on you being healthy.

Apply those "rules" to the following example (adapted from another related post)

Schoolwork is very important for Bob to become a doctor.

Which means Bob's life will be improved by becoming a doctor. Who could be the speaker? The common possibilities would be Bob's parents, Bob's friends, Bob himself.

What if Bob himself doesn't want to be a doctor? So, the situation becomes

Bob's mother says: "Schoolwork is very important for Bob to become a doctor."

Bob says to his best friend: "To be honest, becoming a doctor is not that important to me."

It is my understanding correct?

Answer 1

I mostly agree with you, but I don't find

Schoolwork is very important for Bob to become a doctor.

to be idiomatic, for the following reason.

Important to and important for are not grammatically parallel.

To introduces a complement of important, which tells you who regards the thing as important.

For is not syntactically linked to important at all: it is (an optional) part of the "to"-infinitive clause which may stand as subject of important:

[To study] is important.

[For Bob to study] is important.

Usually, this subject clause is moved to complement position, and the dummy subject it used:

It is important [to study].

It is important [for Bob to study].

but semantically, the clause is still the subject.

I don't find the example idiomatic because it is using a real subject ("Schoolwork"), so it's not clear what the grammatical role of the clause is.