Power bank design, Lithium Ion vs Lithium polymer, single vs series
I understand that you're asking about how to make your pack's capacity useful. One cannot say that your initial approach is wrong unless a requirement is specified. No, it's not necessarily wrong, it depends what you want to achieve.

Let's say you want to charge a phone with a battery which has a capacity of 2000 mAh and for charging it asks for 5V and 1A. If you connect your initial setup to this device, then your pack's drain current will be 5 W/3.7 V=1.35 A. You can divide the bank's capacity with your phone battery's capacity only if your battery charges to 3.7 V, because what you supply to your phone is not necessarily what reaches the battery, it first passes through the charge management circuit. If the phone's battery charges at 4.2 V, for example, then it means that the load battery will have a current of 5 W/4.2 V=1.19 A flowing through it. Your bank would be able to charge the cellphone fully less than 4 times and a half as opposed to 5 times that you would obtain if you divided the pack's capacity with the load battery's capacity.

If I assume that your pack is made of 5 3.7 V Lithium-Ion batteries connected in parallel, each having a capacity of 2000 mAh, I can state that if you connected them all in series, you would be able to charge your phone fully 7 times+ using a buck-boost converter, so you can keep charging even after the pack's output voltage is &lt;=5 V. Note that I didn't include losses in my calculation. I believe that's what happens to: 


  The &lt;10% that do use lipo's use them in series, at 7.4v or even higher


Lithium-Polimer is more dangerous than Lithium-Ion, because it can catch fire or explode more easily if it is not handled properly, but its charging process is less difficult in comparison to the other type. I think the choice should be   based on your experience.