[ir655]

When the voltage rises, the current rises and so does the power.

Aha I see you are staring blindly at a formula without applying it to the real world example of a charger or battery maintainer. As you can see below, the formula the whole world uses to calculate Power (watts).

P = V * I

P = Power (watts)
V = voltage (volts)
I = current (amps)

1200W charger at 12V will produce 100A in theory then. If you increase voltage as you say, current must drop to not exceed 1200W max output of the charger. 

P in the case of chargers and battery maintainers is a fixed value (whatever the sticker says on your charger). 

You forget that the Power output has a cap in this case so you cant just assume that if voltage increases, the rest increases also when applied to real world applications such as battery maintainers and chargers.

I can still be wrong though! I am not an electrician, just an aircraft technician that occasionally work on electrical components of commercial aircraft. In that case I apologize if I am spreading misinformation to members.