This structure is grammatically termed as Cleft Sentence. The cleft sentences are created to emphasize different information denoted by different components of sentences. There is nothing ungrammatical or non-idiomatic with regard to its usage.
The definition of the Cleft Sentence by the dictionary.com:
a sentence in which a simpler sentence is paraphrased by being divided
into two parts, each with its own verb, in order to emphasize certain
information, especially a sentence beginning with expletive it and a
form of be followed by the information being emphasized, as
It was a mushroom that Alice ate instead of Alice ate a
From English Grammar Today (Cambridge Dictionary)
We use cleft sentences, especially in speaking, to connect what is
already understood to what is new to the listener. In a cleft
sentence, a single message is divided (cleft) into two clauses. This
allows us to focus on the new information.
It-clauses are the most common type of cleft clause. The information
that comes after it is emphasised for the listener. The clause which
follows the it-clause is connected using that and it contains
information that is already understood. We often omit that in
informal situations when it is the object of the verb:
A: Sharon’s car got broken into yesterday, did it?
B: No. It was Nina’s car that got broken into!
Focus (new information): it was Nina’s car.
Understood already (old information): a car got broken into
A: You’ve met my mother, haven’t you?
B: No, it was your sister (that) I met!
Focus (new information): it was your sister.
Understood already (old information): I met someone in your family
Is it August that you are going on holiday?
Focus (new information): the month August?
Understood already (old information): you are going on holiday
When a personal subject is the focus, we can use who instead of that.
We often omit who in informal situations when it is the object of the
It was my husband who (or that) you spoke to on the phone. (or It was my husband you spoke to on the phone.)
When a plural subject is the focus, we use a plural verb but It + be
It’s the parents who were protesting most.
We can use negative structures in the it-clause:
It wasn’t the Greek student who phoned.
Wh-cleft sentences are most often introduced by what, but we can also
use why, where, how, etc. The information in the wh-clause is
typically old or understood information, while the information in the
following clause is new and in focus:
A: I don’t know what to cook for them? I don’t know what they like.
B:What they like is smoked salmon.
Understood already (old information): we are talking about what they
like to eat
Focus (new information): they like smoked salmon.
A: This remote control isn’t working.
B: What we need to do is get new batteries for it.
Understood already (old information): there is something that we need
to do to fix the remote control.
Focus (new information): we need to buy new batteries.