Is engine damage due to a fan blade failure irreparable?
This depends on the failure: A fan blade can be damaged by birds, debris, or aircraft parts (pitot probe for example).  In this case the blades are dented, in which case it is possible to replace the damaged parts, inspect the engine and re-use it.

For this kind of damage it has to be disassembled and inspected by the engine manufacturer.

Inspection of blades is done with a microscope: For example, I have seen an HPT blade declared unserviceable because of a small scratch.

Obviously if the repair costs more than a new engine you don't repair the old one.

Many more things can happen in startup:


The engine is run on full power
There is a lot of possible interactions (like birds for example) that you don't have in a steady cruise at 40,000 feet.


Aside from debris, you can also have a compressor stall like this.