My understanding is that the limitation is related to Vmcg issues, particularly near V1. Once airborne and above V2 you can safely increase thrust above the fixed derate, all the way up to Max TO if necessary.
Once upon a time we had a note in our 777 Flight Crew Training Manual to that effect. The note has since been removed, but in the sim we still practice increasing thrust in the event of an engine failure. Given the hugely reduced thrust settings we use for most take-offs, the increased thrust following an engine failure provides much better single-engine climb performance.