Why are so many batteries 3.7V?
The voltage is dependent on the materials used in the cell chemistry and cannot be chosen per se.
3.7V is typical for Lithium chemistries. Similarly, 1.2V is typical for nickel-cadmium (NiCd), 1.2V for nickel-metal hydride (NiMh), 1.5V for alkaline batteries, and 2V for lead-acid.
Notice that 3V and 9V are multiples of 1.5V. 3V and 9V are not customized values simply because they are round figures. They have been chosen as such since they are batteries constructed from stacks of alkaline cells. The same is true for 6V and 12V lead-acid batteries made from stacks of 2V cells.
So, why are there so many lithium batteries today? They are rechargeable, have no memory, and have superior qualities with respect to energy, power density, power volume, and weight compared to the other forms of batteries mentioned above.
NOTE: Memory is a behavior that some battery chemistries display wherein their capacities decrease every time you recharge them if you are not properly maintaining them or discharging them to near-empty before recharging them. Think of it like letting the old gas at the bottom of your gas tank congeal and solidify and then filling it up again. You get less gas into and out of it every time.