I expect age will affect power output hardly at all but wear and tear can affect it and wear and tear occurs whenever the engine is running, more so under some conditions than others and more so on some engines than others. 'Some' engines could start out seemingly identical, how they are used / driven / looked after (servicing etc) and a massive helping of pot luck (unpredictable / chaotic type stuff) will affect how use causes wear and tear. Wear and tear can occur at a different rate than use.
The main bits in the engine are metal, keep the metal soaked in oil and it'll still be in nearly as new condition after many years. Not all engine bits are metal, there are bits like valve stem oil seals that can go wrong in time, if they let oil into the intake charge it'll burn oil and probably be down a bit on power due to that. Bits like cam chain tensioners/guides would probably go wrong in time before the metal bits would but we'd expect them to last many years in storage too.
If we had a new engine that made 240bhp and a 50 year old same model engine than only made say 180bhp, then if we consider that the old engine is down on power by 60bhp we could ask where that 60bhp went. If that 60bhp went to internal friction we'd soon know about it because the engine would either soon start to break up or suffer localised internal overheating issues, so the power loss must be either due to either valve train related breathing issues or piston ring blowby, but we'd normally have easy ways of knowing if it was ring blowby.
I reckon power losses with increasing wear and tear / mileage are mostly due to valve-train related wear such as cam profiles / cam followers getting worn, valve seat recession and cam chain stretch... aspects that affect the engine's breathing so hence volumetric efficiency and power, but as said above these are normally things that happen with wear and tear not age.
In some ways age and use can be a positive over a new engine... At one time racers used to prefer to build a race engine using an old block that had already been through many cold/hot cycles because the cold/hot cycles helped relieve internal stresses in the block thus making it less likely to fail. Not sure if that would still be the case today though because on the flip side there is metal fatigue due to continued slight bending of the metal going against the more used block. That said it's not normally the block that fails.
Post crossed with
@Highway Dave 's