To go to great lengths is perhaps idiomatic, but easily understandable. The AHDEL defines length (or lengths) as:
- *often lengths) Extent or degree to which an action or policy is carried: went to great lengths to prove his point.
Many other dictionaries give this definition as well.
You ask, why not "go great lengths"? It's not a place to which someone has gone, it's a degree to which someone has gone.
Even if it were a place, it's usually an end point.
"I went all the way to the top to get this assignment for you."
If you want an idiom that is fun to contemplate,
to bend over backwards
means the same thing.