it seems intuitive to use much higher voltage to achieve higher current - Actually, no. Voltage and current are independent. Increase one and you can keep the other steady or up or down. The thing that is true is that increasing voltage (or current) while keeping current (or voltage) steady will increase power. But that really isn't the issue when it comes to an electric chair.
I don't know why particular voltages have been picked for the "electric chair" (not sure I want to know...). But I can explain a bit about voltage vs. current vs. power, and the deadly combinations thereof.
There is voltage (think 120V or 240V in most homes). There is current (think 2A for a phone charger output, 12A for a hair dryer, 30A for a clothes dryer, etc.) Then there is power which is, essentially, voltage times current.
- 2A output of a phone charger at 5V DC (DC vs. AC is relevant, but after this line, I'll ignore it as it makes little difference in the grand scheme of calculations here) = 10W (output, a little more on the input side due to conversion losses)
- 2A of electric lighting (e.g., 4 "60W incandescent bulbs") at 120V = 480W.
So the power produced at higher voltages is higher than at lower voltages. But the current is not necessarily higher. For example:
- 12A at 120V = 1,440W of power - that's the most you'll get on a standard 15A circuit for continuous usage. (More or less, sometimes calculated based on 125V = 1,500W).
- 6A at 240V = 1,440W of power. 1/2 the current to get the same result (in terms of heating or lighting or motors or whatever)
- 12A at 240V = 2,880W of power. Same current, double the voltage = double the usable power.
All of this matters a lot in design of appliances. The reason (in the US) that dryers, water heaters, heat pumps, etc. use 240V is to get more power without using a lot of current so that wire size can stay small (among other reasons).
Now back to the "electric chair". It really only takes a very little bit of current through the heart to kill someone. That's why Ground Fault Circuit Interrupters work at incredibly low current - typically 6ma - 8ma. The same current at low voltage (e.g., 9V battery) won't normally do anything except a slight tingle. But mains voltage (even 120V, but it gets more dangerous with higher voltage) can more easily make its way through the skin, especially if wet, to complete a circuit through a human body.
The "electric chair" is a big contraption, designed, I suspect, both to intimidate and also designed before a lot of the details of how electricity works (and how it kills) were understood. Wet both hands of a death-row inmate, attach one hand to neutral, the other to hot and flip the switch on a standard 120V circuit and I suspect the effect would be as immediate and deadly as thousands of volts through a big contraption.
Remember this when your kitchen or bathroom GFCI trips and you complain "why'd this stupid thing stop working again, maybe I should just plug it into a different, non-GFCI, receptacle and stop these annoying trips". Water + electricity kills.