Its a lot of momentum to fight against; the solution is going to need to be extremely compelling to compete against the existing USB/vehicle DC power solutions.
Rather, the issue is that what is going on inside the phone. In most modern phones the input voltage is fed into a monolithic power management IC which provides the numerous voltages required to run the device, handles power on timings, and often contains the batter charger. The unit in the GN is linked below [0].
There are various ways to hook these up, but a popular method is to only supply the device power rails from the battery. If you've ever ran your phone completely dry, plugged it in tried to power it on, and watched it only start up for a couple seconds and die again, its because the battery didn't have enough charge to get through boot up, which uses a lot of power.
In other words, even when your phone is plugged into the wall, its probably still running on the battery. For the same reason, most newer smart phones can't be powered on without a battery in them. Its also why a phone using a lot of power while plugged in gets very warm around the battery, you are pouring power into the battery just to remove it again, the inefficiencies in the process = heat.
Thus, what it really comes down to is the ability of the phone to discharge its battery faster than it can be charged. The limit of how fast you can charge the battery can be caused by limited power (computer USB port), limits in the charger or simply by the physics of charging a li-ion without causing damage to the battery or the user.
In this case, without doing the math on it, ~5W is probably about the limit of the charging IC linked below, depending on charging mode. Just a guess though, it could also be the limit of the batteries ability to charge.
I have seen phones that can really switch to running on actual input power, but these seem to be less common now. It requires addition components in the form of a power switch and often a regulator. More importantly it takes board space and costs money.