I must be mixing things up when I think of power in watts in this respect. I guess that explains why none of these tools consider voltage in the calculation.

But the power is expressed in Watts, so nothing wrong with your understanding here. What I feel might be the case with your understanding is the common misconception many beginners fall under and that would be, despite knowing the Ohm's law in general, still thinking about the voltage and the current as somehow "decoupled".

Let's attack this from a different angle: if the resistance of the given length of trace is constant (and we ignore the temperature effects now for the sake of simplicity), both voltage and current are strictly dependent. You change one, the other follows. So, let's assume you have a trace whose resistance measures 2 Ohms end to end. If you apply a voltage difference of 5V across it, the current of 2.5A will flow. To put it different way, you NEED 5V to "force" 2.5A current through 2 Ohm resistance so there's no point stating both. Continuing, in this case it is a mistake to argue that "5A@5V is more power than 2.5A@5V" or that "2.5A@10V is more power than 2.5A@5V". Your resistor is 2 Ohm so you simply cannot assume any arbitrary voltage and any arbitrary current. If you measure 5A of current, that means there's 10V across your trace's ends. If you measure 3V across your trace, that means there's 1.5A flowing through it. There is no magical box that lets you dial both of them independently through a given constant resistance.

I think at least some of this misunderstanding results from the way DC power adapter manufacturers specify their parameters. Far to many times have I heard that "you cannot use this power supply with this device: it provides 5V, 2A and the device needs 5V, 1A so it will burn out". Once more, not the case. How you should read the DC power bricks' specs is: both of them are constant 5V voltage sources so both of them will be good for my device that needs 5V at 500 mA. Where they differ is, the beefier one should be able to safely provide a current of up to 2A once loaded with an equivalent resistance low enough for the 2 amps of current to be able to flow at 5 volts and that would be 2.5 Ohms.