If most use some sort of li-ion battery, and those batteries like to be charged in CCCV format how can my phone charge just fine at 5V, 500mA or 5V, 1A or 5V, 1.2A just fine (actual current delivered, not power supply capabilities)? It seems the current is not constant. If I made a 5V, 1A battery charger it is recommended to not use a 5V, 0.5A supply since the charger was designed for 1A.
Do phones just have really complicated charging circuitry that differs from the standard li-ion charging ICs? Everyone can either charge their phone with USB at 500mA or use a wall adaptor for a faster rate.