One other aspect of increasing engine power in a twin is that it allows PC 1 profiles at higher AUM so more bums on seats in the cabin.
I think in the Twin engine world, this is the primary reason for increasing power - as has been noted you typically can't use the maximum power from both engines AEO due to transmission limits. The confliction that arises is that turbine engines operate most efficiently close to their design point, at high Ng, so for best AEO fuel efficiency you want the engines to be running 'flat out'. But, that means if you lose one you take a big hit on power remaining. Conversely, you can have powerful engines that are 'barely working' when AEO, but are able to pick up most of the load OEI, which results in good payloads but poor AEO fuel efficiency. Probably the best example is the S76B vs the S76A+, although modern design of engines and transmissions is closing the gap.