Also, reduced density has some benefits for Optimum level.
The less the density or the more the temperature the more the TAS for a given Mach, which gives better specific range.
Density is very "good" at low level, and yet the optimum levels are very high, because of specific range. Given that fuel flow is approximately proportional to thrust, for the same EAS you have more TAS at altitude while having the same drag, which needs the same thrust. We get more miles for the same money.
However, for a constant mach number EAS also increases for with increasing temperature, which will increase drag, I suppose, plus compressibility effects compared to same EAS at very low level. Some more thrust is needed with increasing temps, I guess.
It seems to me that there is a direct relationship between MAX and OPT levels, like they depend on the same things. When I fly at MAX, I have noticed that my engines are giving me already maximum thrust. I have literally advanced the thrust levers to TOGA and the N1 did not increase a bit of a bit. I don't know if engine temperature limits play a part in that, or if its something else like rpms, but probably the engine at that condition has more thrust specific fuel consumption than at the optimum level, to the extent that it pays flying at that level instead.