Samsung devices (this is a Note 5 btw) limit charge current when the screen is on, probably to reduce the heat generated by the device (though I would much have preferred using actual SoC and battery thermistors to dynamically throttle this), but under load the device seems to be able to pull power from the charger as needed. When the screen is off, the battery charges at full current but beyond 80% usually slows down below the rated (Entering CV phase from CC) However, the battery chargers on all devices might be set to lower than 4A or whatever the rating is, and without the system load it won't hit the full input current.
Also note that typically devices (esp. Apple) expect 4.8V or so to keep increasing current draw. Most cables are quite thin and unable to meet this requirement, dropping under 4.7 at 1.5-2A. The charge controller will likely then throttle the current to stay above this threshold.
I have had Anker PowerLine (2?) USB A to Micro B cables that were able to handle 4A (rated 2.4) before falling to 4.85V (tested with 5 port usb charger modified to bypass load side switches so theoretically 12A output). Neither connectors, cable, or other components became hot or warm.
Most other cables can barely deliver 4.76V at 1.7 ish amperes.
This probably correlates with parent comment's experiences.