14AWG can sustain 16A of continuous current under most common home conditions.
In a three phase system three 14 AWG wires can supply little over 10kW without exceeding those limits.
Three phase system are more efficient if you are looking at saving wire.
You add one wire but you triple the available power.
But that's not the end of advantages. After rectification the voltage never goes down to 0.
So the filtration needs are lower. Less capacity is required to achieve decent ripple which means lower cost.
Wikipedia explains it rather well with simple graphs.
https://en.wikipedia.org/wiki/Rectifier#Three-phase_bridge_rectifier_uncontrolled
The thing with power over cable is that cable losses are calculated with Power_Losses=Current*Current*Resistance.
And Power=Voltage*Current. Twice the current means four times the losses. Double the voltage, halve the current and you get four times lower losses.
So if you want to make more efficient transmission lines you increase the voltage to decrease the current.
Chinese right now are using 1100kV transmission lines for this exact reason. Plenty of coutries around the world prefer the 220-240V standard at home because of savings.
The simplest comparison.
USA uses 120V, Europe 230V.
At 16A it means 1920W for USA and 3680W for Europe.
Same wire used in both cases.
As for car charging stations I know a guy from univeristy who was making his engineer's thesis based on a project of such charger. So he got me interested in the subject.
For europe the chargers are simpler because they don't really need much power conversion to happen.
Three phase 3x400V gets rectified to around 565V DC (peak, will drop slightly under load).
Most fast chargers use 400-800V DC. The voltage is already there.
For 240V AC supply based from two phase system (used commonly in US) to achieve a similar voltage you may use a voltage doubler (simple, two diodes, two capacitors) but also an active boost converter.
The second beeing "nicer" as the apparent power (rectifier with capacitors is drawing non-sinusoidal current, creating distortion) is far lower, allowing savings on infrastructure (wiring, transformers).
Well, in most cases charging stations have their own dedicated transformers, stepping down from 15-30kV to supply all the charger with the much needed power.
So in the US I guess that they simply used higher voltages on transformer output to allow simpler power conversion.