My understanding is that the slow charge is to extend the life of the battery and prevent premature (even catastrophic) failure of the battery.
If you only charge your phone, the power supply isn´t a real problem, finally 700mA@5V is enough to charge the battery in about 2h, well at least in theory.
There are only 2 problems:
The main problem might be, that you want to use your phone for something while it is charging. And the device can consume most of the power for the actual usage, so not much is left to charge the battery.
A minor problem are the charging-characteristics of Li-Ion-cells. It is not possible to fully charge a Li-Ion-battery under 3h.
Charging is divided in 2 stages.
In the first stage charging should be done at about 0,5-1C. C in this case means the rated Capacity of the battery, so a 1,6Ah-cell should be charged with 0,8-1,6A
This stage lasts until cell-voltage is about 4,2V
With 700mA@5V the power-supply can only give about 0,8A @ 4,2V which is just the lower limit of the recommended charging-current. In reality it is a bit higher most of the time, as the voltage only tops at 4,2V. Cell-Voltage shouldn´t be under 3V, which is probably the limit where the phone switches off to prevent over-discharging. So during the first charging-stage from a completely flat battery voltage will rise from 3 to 4,2V and at 3V the power-supply can at least give about 1,3A.
This first stage lasts from one (when charging with 1C) to two (when charging with 0,5C) hours.
As the voltage rises quite linear, we can assume an average voltage of about 3,6V which means an average current of about 1,1A or 0,68C, so with the supplied power-adapter stage 1 (from a complete flat battery) must be at least 1,5h. But only if you are not using the phone at all.
This will charge the battery to about 75-85%
After this the charging-device switches into stage 2, also called the saturation-stage. In this stage the voltage remains constant at the set limit (usually about 4,2V) and the charging-current constantly drops. The saturation-stage lasts at least another 2h to get the missing 15% of charge into the battery.
The conclusion is:
Charging will get slower the higher the charging-level already is. In stage 1 because the voltage rises and the power-supply can not provide enough current, and if we are already in stage 2 because the battery can´t be charged any faster without risking damage.
And using the phone during charging will significantly increase the charging-time significant.