Do all micro usb cables support fast/rapid charging?

In other words, is the fast charge feature dependent on the wall plug, the cable, or the phone?

 

In most simplest terms: yes.

 

Short answer: The cable.

Long answer to explain the above answer:

Fast Charging Cables Vs. Regular Charging Cables
Even though they are not physically distinguishable, there are different varieties of USB cables. Yes, USB cords affect how quickly your device’s battery charges to 100%. To get the fastest charging speed from a device with quick charging technology, you usually need to use a fast-charging power brick and a fast charging cable.

But what makes a standard cable different from a fast-charging cable? At any given time, the amount of power is transferred to your device’s battery. Fast charging cables can deliver more current to fill up your battery’s capacity faster than conventional cables.

Regular USB cords deliver roughly 2.5 watts of electricity to your smartphone’s battery, whereas fast charging cables can deliver up to 120 watts of power (depending on the manufacturer and type of your smartphone). You will not receive fast charging speed if you use a conventional USB cable and a fast-charging power brick/adapter to charge a smartphone. This is because the amount of electricity a conventional cable can transfer to a device is restricted.

Now that you know the difference between fast and regular cables, let’s move on to identify a fast charging cable.

How to Identify a Fast Charging Cable
As previously stated, the quantity of electricity a cable can transport determines how quickly it charges. This is proportional to the size of the wire within the cable; it’s just physics. Because a wire’s current carrying capacity is limited, a larger wire can carry more current.

A typical USB cable’s wires are usually standard-sized 28 gauge wires; however fast charging cables include bigger/thicker 24 gauge wires, allowing more current to be given to a battery of the same capacity.

 

Combination of all three.

You could have a phone that is capable of being fast charged, a cable capable of handling the load of fast charging, but then a charger that does not output the proper wattage\amperage to fast charge and the phone would NOT fast charge.

You need all the right equipment. There are cables that are not rated for it and thus won't support it even when the charger can and the phone can.

In the simplest terms, you need all the pieces to be rated for and capable of to actually have fast charging work like it should.

 

Micro USB doesn't fast charge in the sense that the Charger and Device negotiate power and charge at a higher voltage.
USB C with PD on the other hand does. on USB Micro you may get 5V 1.5A maybe 2A tops.
USB C with Power Delivery (PD) can get 5V, 9V, 12v and even 24V. For example my Pixel can charge at 9V 2A (18W)
also the cable needs to be up to snuff, you cant just get some regular old Type C cable and crank 60 Watts through it.
Check out the USB-if website for more on the PD Charging standard.

**Edit, I believe Qualcomm Quick Charge can charge Micro USB at a higher rate.