Instead, we can create a pair of entangled qubits (which is easy to do - just a single quantum gate), as one would when teleporting a qubit. We then apply the computation to one of these qubits, and try again with a new pair of qubits if it fails.
Once we have successfully applied the computation, we can teleport our "expensive" qubit Y using this entangled pair. The result is that we now have Y with the computation applied, but there is no risk of losing Y's state.
The details are rather more tricky (only certain computations can be used, some require a correction after teleportation etc.), but this basis can (and has) be built on to develop, for example, fault tolerant quantum computing.
1) Perform the first step on a qubit (repeat if failed)
2) Your friend performs the second step on their qubit (repeat if failed, but no need to repeat (1))
3) Teleport your qubit to your friend
4) Your friend performs a simply operation on their qubit
After this, the state of your friend's qubit is now the result of applying both operations. But each sub-step can be redone without affecting the result of the other, so mistakes are easier to correct. So in this case, "your friend" might refer to yourself - the important part isn't teleporting the qubit somewhere elses, it's that the computation is less error-prone.
However, you remember that your "friend" has this equipment at his/her lab. You also happen to share an entangled qubit with your friend. And you know that you can call your friend on the phone.
Rather than mail the qubit to your friend's lab which could be in a very remote location, you use quantum teleportation to send its state.
This way your friend receives your qubit without the qubit having traveled through physical space.
Can you clairify the second reasons to "bother" with it? I mean, if it's difficult for me to perform the operation, it's presumably equally difficult for my "friend" to do it (and subsequently "teleport" the result to me), so why not just do it myself?