Electricity doesn’t really work in a way the host can “push” current

On a basic level this is precisely how electricity works, a power supply literally pushes electrons by creating a difference in electric field magnitude between two points; or, in other words, by applying an electromotive force to electrons; or, in other words, by creating a voltage between two points. A load then does something with those electrons that usually creates an opposing electric field, be it heating a wire, spinning a motor, or sustaining a chemical reaction within a battery. The amount of power produced by the source and released at the load is proportional to (voltage) * (number of electrons being pushed by the supply per unit of time); usually, this is the limiting factor for most power supplies. They can hold a steady voltage until they have to push too many electrons, then the voltage starts dropping.

Edit: I see what you mean now. Yeah, for a given voltage, it is the load that determines the current, so there's no safety issue with this for the load. However there could be issues with the cables. IIRC there was an issue with noise being introduced by higher current draws that meant you couldn't charge and transfer data at the same time with some cables.