That is not an issue. PCB traces (and other copper foils stuck to surfaces) are capable of carrying more current than wires of the same cross-section area because the surface they adhere to carries away some heat.

A common adhesive copper foil is about the same thickness as a standard PCB trace, about 35 µm. According to for example this online calculator, a PCB trace of that thickness and 2 mm wide can happily carry 2 A.

A trace of that width and thickness gives the cross-section of 0.07 mm2. A standard copper wire with the same cross-section would have a 0.3 mm diameter and a capacity of about 1.3 A.

The point where the foil connects to the battery contacts is a different issue. You have to make that contact very reliable for the currents that the phone can take in heavy use. Just sticking the foil to the contact and hoping for the best will not cut it. This is why soldering is the best option.