It seems like charging chip limits total consumption to 3.5W.

Phone consumes ~420mW while cpu is idling, screen is on and wifi off, as battery charger chip reports. Charging in the same settings with battery at 25% gives (-3010mW), so total is about 3.42W. At 5V corresponding current will be 700mA if DC-DC coverters are used. Then there are losses in conversion (10-20% I guess), so current draw from charger should be about 800-900 mA.

If charger is high quality, it should be able to handle some overdraw. If it's not, then it's output voltage may be with ripples and that may confuse charger chip and led to improper charging cycle. That's pure speculation on my part since i haven't read any hardware's datasheets.