However, I've always thought about a wire's capacity by total power transmitted, not just the current.

That is indeed your prerogative. You have every right as an independent human being to think how you like.

However, it's not useful to the rest of the engineering community, because multiplication is easier to do than division.

Of course, people want to shift power. However, voltage for any given system tends to be standardised, at 120, or 240, or 48v, or 33kV. Working in a particular distribution system, if you want twice as much power, you need twice the current rating for power. Easy peasy.

Wires have a maximum voltage determined by their breakdown, which is a function of insulation thickness and quality, and wire diameter. Once you've bought your reel of wire, there's nothing you can do about any of those terms.

A wire tends to have a minimum insulation thickness given by robustness, regardless of how low the rated voltage is.

Wires have a maximum current determined by their heating and cooling per unit length. If you string a single wire, or run a bundle of wires in an insulated conduit, the thermal resistance per unit length will be radically different. That's wire the tables give different entries for single or bundled wires, and often different ratings depending on ambient temperature.

Imagine how it would be if as well as multiple columns for single versus bundled wires, the tables were of power, and had different columns for 12v, 120v, 240v.

However, I've always thought about a wire's capacity by total power transmitted, not just the current.

That is indeed your prerogative. You have every right as an independent human being to think how you like.

However, it's not useful to the rest of the engineering community, because the wire thermal limitation in amps is independent of the system voltage, and multiplication is easier to do than division

Of course, people want to shift power. However, voltage for any given system tends to be standardised, at 120, or 240, or 48v, or 33kV. Working in a particular distribution system, if you want twice as much power, you need twice the current rating. Easy peasy.

Wires have a maximum voltage determined by their breakdown, which is a function of insulation thickness and quality, and wire diameter. Once you've bought your reel of wire, there's nothing you can do about any of those terms.

A wire tends to have a minimum insulation thickness given by robustness, regardless of how low the rated voltage is.

Wires have a maximum current determined by their heating and cooling per unit length. If you string a single wire, or run a bundle of wires in an insulated conduit, the thermal resistance per unit length will be radically different. That's why the tables give different entries for single or bundled wires, and often different ratings depending on ambient temperature.

Imagine how it would be if as well as multiple columns for single versus bundled wires, the tables were of power, and had different columns for 12v, 120v, 240v, and then didn't have a column for your voltage.