It's not cost savings but ecological consciousness. What if everyone turned their devices off when not using them? Call me a treehugger, I wear it with pride.
And so you should. Ecology is not a joke.
But I think it is more complicated than that. Turning things on and off constantly has a larger environmental impact in the long run. As electronic products (even the best made ones) are far more likely to develop a fault on power on, mathematically, your odds of having a fault on a product multiply for each item you do this for.
And when an item does fault, the impact of the shipping to and from a place of repair or the impact of a manufactured replacement is greater (as is the cost - but you already said that was of no concern to you) than the impact of having the unit powered on all the time.
Let us say you have a 5 box Naim system and each unit has a 10% chance of failing in a 10 year period if powered on and off twice a day every day. Probability is calculated as ratio multiplication so you would have a 50% chance of a box in a 5 box system faulting in 10 years. The result of that fault is transport by various vehicles to Naim and back, the manufacture of replacement parts, and or the manufacture of a whole new unit. Both the monetary cost and environment cost are likely to be far larger than the cost of the idling current of the units left on 24/7.
Of course, you can power them on and off every day and they might march on for 40 years without a problem. But if the same power off policy is used throughout the home, you won't beat the odds forever and it becomes more of an environmental issue with lower cost, more modern, very lower power consumption devices that are not built to the same standard as Naim. Low cost, low power domestic appliances have a very bad ratio of energy consumed when idling against the energy cost incurred for repairing/replacing a failed unit. Ideally, you want things to be as energy efficient as possible and to use them in a way that then makes them last as long as possible to reduce the demand for related logistics and the manufacturing chain.