How come charging a phone with less current is just slower?
Typically:

It just monitors the voltage of the power supply. If that drops too far (typically, for USB chargers, below 4.8 V), it reduces the current sink into the battery.

A smarter charger might "scan" the "tolerable" input voltage range and find the sweet spot where most power can be drawn from the supply, but really, supplies are designed to be low output impedance, so, the closer to a current maximum you press them, the more power you'll transfer (basically: maximum power impedance matching means that your charging circuit should look like a small resistor value, subject to a load limit).