I never have problem charging @ 2.0A on all my phones regardless whatever charger it came with. In fact my old Nexus 4 it came with a 1.0A charger that I never use, the phone is still working fine after 5+ years.
The cable does play a part in the charging speed as well. Usually the cable that came with your phone is of higher quality and can charge quicker because it has more wiring to carry the electric current than the dollar-store cables (Correct me if I'm wrong). Also the shorter the cable the quicker the charging.
If you are shopping for spare cables that are optimized for charging check the AWG rating. The lower the better (yes it seems counter-intuitive...idk why). Normal cables are 28 AWG, there are better ones at 24 AWG or even 22 but these are more expensive.
