I have Pi3b and Pi 3b+ which draws even more running totally reliably on 2A power supplies.
BUT I do use my own home made heavy guage USB cables between the power supply and the Pi. It cannot be stressed how important the USB cable is. It is the volts at the Pi that matters not the volts coming out of the power supply.
Assume a 1A draw.
A typical reasonably quality USB cable might have a round trip resistance of 300 mOhm. That is 300mV drop taking a 5V supply down to 4.7V below the spec limit.
A poor USB quality can have a round trip resistance of 1 Ohm leading to a 1V drop and no chance of operation.
My home made cables have a round trip resistance of < 75 mOhm and minimal voltage drop.
Note that some power supplies e.g the official raspberry one deliberately source a slightly higher voltage (5.2V) to try to compensate for the cable loss. These often have the cable hard wired in at the PS end and use heavier guage wires.