you might want to purchase a heat sink for the CPU from one of the many vendors that seem to have them... I've heard that RPi 3 can overheat if you do too much for too long with it. It's fine when idling, or flipping I/O bits on/off on occasion, but if you're number-crunching, consider a heat sink.
you realize that the USB charger spec is 500ma, right? Although most USB chargers seem to be able to supply significantly MORE than that, if you're seeing a voltage drop below 5.0V then it's most likely under-rated.
What are you possibly doing that requires more than 1.5A ? I suggest that whatever 'power piggy' device you're trying to power with the RPi get a separate power supply just for that load...
again, what are you trying to drive with the RPi ? if the CPU is overheating, you can try a heat sink, but 1.5A for an RPi is excessive [your other loads are drawing too much current in other words].
If you have USB peripherals plugged into the RPi, try unplugging them. That might be your problem.
The below applies to A/B/microB sockets not USB-C sockets.
The original spec for USB said that what is now known as a Standard Downstream Port can supply up to 500mA. This is a USB port that has full data transfer capabilities as well as providing power. The standard USB socket you see on a laptop etc. Normally the power is managed by the hub controller with up to 500mA per socket.
Charging Downstream Ports can provide up to 2A as well as full data facilities. You typically find one CDP amongst the sockets on most modern laptops.
Dedicated Charging Port is a charger with no data. This typically a wall wart type of device. There are chargers that do not follow the DCP standard but still work fine.
The USB charging spec provides a method for a device to talk to the port to determine the charging characteristics before USB enumeration occurs.
I have a variety of wall wart chargers at 500mA, 700ma, 1A, 1.3A, 1.5A and 2A. A smart device that implements the USB charging spec will pull as much current as it needs up to the limit of the port type it identified. So up to 2A for a proper CDP or DCP and 500mA for an SDP or unidentified port.
I'm pretty sure you're wrong there, especuially if your case is already somewhat open. The biggest barrier (measured in K/W) is usually the surface between solid and air and that's just where the sink comes in. In a closed case you have two additional such surfaces between the case and internal and external air. But then too the heat sink means a lot, as the surrounding air inside is already hot and you need to get as much out of the small difference as you can.
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