Once in a while, I would encounter "reversed" sentences like this:
お腹が痛くなったのは食べ過ぎたせいです。
In my head, I would translate this to English to
That my stomach hurt is because I overate.
Not the most natural way of saying things, but still acceptable. But recently, I have been seeing sentences like "~のは、〜から・ので・ためです" more often, and it got me thinking, how often do Japanese say things this way? How does this affect the emphasis in the sentence if it is written this way:
食べ過ぎたせいでお腹が痛くなりました。
Your example sentence is a cleft sentence. It's a very common pattern.
食べ過ぎたせいで、お腹が痛くなりました。
My stomach hurt because I overate.
お腹が痛くなったのは食べ過ぎたせいです。
It's because I overate that my stomach hurt.
Broadly speaking, this の is a kind of nominalizer (that's why you got an "acceptable" translation). But usually you should translate this ～のは～だ pattern using the grammar of English cleft sentences, which look like "It is ～ that ～" or "It was ～ who ～".
How often do Japanese say things this way?
As often as English speakers say "It's because ～ that ～".
