Powerbanks are not made for powering electronics. They are made for re-charging batteries.
This is important because these two tasks have some requirements that are at odds. Most significantly, in powering electronics it necessary for the supply to be responsive to rapid fluctuations in current draw, but the exact opposite is true with regard to recharging batteries; sudden fluctuations in current shouldn't occur and the circuitry of the power bank will, at the least, not be designed to be responsive (such that the voltage will drop in response to a sudden demand for current). It might even be designed to prevent surges in current.
The primary target of powerbanks is of course mobile devices that use batteries rated somewhere between 3 and 4 volts (I think 3.2 and 3.7 are common). If you take a powerbank apart, you will find that they use the exact same types of batteries albeit bigger (i.e., capable of storing more energy). This means the voltage is being stepped up to 5V to fulfil a generic standard -- that of the USB connectors they use.
However, they don't really need to maintain a steady 5V and as they discharge this will probably drop. It may also wax and wane, as per the Q&A linked above.
Point being, don't expect them to work well for your application. If you want a stable portable power supply for a Pi, you should use something that is explicitly intended to power 5V electronics from lower voltage batteries. These are much less common than power banks but you should be able to find them at hobbyist electronics retailers. They are usually called boost or step-up converters (powerbanks use them too, but again, these are not all created equal).
You might have better luck with newer USB C powerbanks, which must deliver more current to provide faster charge times -- but maybe not, since again, the higher quality the item the more likely it is to smooth away rapid fluctuations in current draw.
I've used powerbanks a bit with various pis and my experience is that they are okay with most models depending what else is connected -- although they do not not live up to their mAh ratings, which are usually derived from the batteries inside them and indicative of how much charge they can provide simililar lower voltage batteries. I.e., they do not indicate how long the bank will last at 5V.
However, I noticed they are not so good with a Pi 3. With no peripherals, a 3's power led will almost certainly flicker when booting on a powerbank, indicating the supply cannot deliver in the context of the rapid fluctuations in draw which occur when the device is booting.