The reason why we hash the concatenation to get the parent is because we can provide a proof of inclusion. Specifically, we can show that L is represented in the parent, P, by revealing R. That is, if we want proof L is represented in P, the producer of P can show us R and let us know that L is the left child of P. We can then combine L and R to produce P and have proof that L was used to produce P. If L is not represented in P, being able to provide R would be the equivalent to providing a hash pre-image, which we know is very difficult. This is what we mean by a proof of inclusion.
The reason why we hash the concatenation to get the parent is because we can provide a proof of inclusion. Specifically, we can show that L is represented in the parent, P, by revealing R. That is, if we want proof L is represented in P, the producer of P can show us R and let us know that L is the left child of P. We can then combine L and R to produce P and have proof that L was used to produce P. If L is not represented in P, being able to provide R would be the equivalent to providing a hash pre-image, which we know is very difficult. This is what we mean by a proof of inclusion.