Actually, also had in mind power supplies in PCs, which, I believe, are often "powered" without the power switch being on. Routers and switches, likely have the power switch (if they have one) before the power supply.
In any case, think of electricity (somewhat) like water, and a power switch is like a gate value that can open or close very quickly.
Then consider how close such a value is to the water wheel. The closer the value, when opened, the faster the "pressure" will travel to the water wheel.
Keep in mind, though, electrical "pressure" is very fast, i.e. a significant fraction of light speed.
For just powering device, the time difference would be very, very small; except for really high speed computing, distance likely doesn't matter.
The other aspect of electrical power, what if the "pipes" to the water wheel don't already have standing water in them, i.e. you also need to fill them when you open the value.
In other words, for the water wheel to "work" it needs both water and "flow". The closer the value is, to the water wheel, the sooner the wheel can work when you open the value.
In routers and switches, etc., we often use AC power feeds, but actual power is often low voltage DC generated from the AC. Believe this too takes some time, and so a power switch between a power supply and a router's or switch's circuitry, I believe, might provide what the device needs a bit sooner than if the power switch, or plug, is upstream of the device's power supply.
Again, for switches and routers, I think it very unlikely, having and using a power switch makes any practical difference vs. connecting a plug.
The only practical thing, I suspect, that might make a difference is doing full power cycles (power switch or plug) vs. warm power cycles (e.g. Cisco reload). The former, I believe, is more stressful on the hardware. (Like how an incandesce light bulb, which seem more likely to "burn out" when you turned it on.)
