If I may add to Mutt's observation .. include aircraft with pilot limited thrust .. ie those where the pilot can push the levers to command greater than rated thrust. Same concern/result as with derate.
The problem is at the lower weights with low speed schedules. In general, unless there is another problem involved, a simple engine failure ought not require that the levers be moved ....
To use more than 5° of bank is no problem as long as you meet the required climb gradient
some considerations..
(a) 5 deg is the max permitted for certification to keep everyone honest
(b) Vmc speeds are very sensitive to bank
(c) likewise climb performance OEI
(d) given that the optimum bank is somewhere around 2-3 degrees ... a substantial increase puts you in a significant sideslip situation at low speed .. is that a good idea ?