Well who ever at micro robotics that gave you the 5.1V advice, Give him bells 
The Pi has always been sensitive when it comes to voltage.
Besides the PI 4 that I have posted earlier on using the 3D printed enclosure. I also have a Pi2B, connected to a 3.5" adafruit LCD, with a 3W audio amplifier running retro pi. Running retro game emulator on a PI2 most certainly is a good way to punish the CPU and draw more current. Add 3.5" LCD and an Audio amplifier and some Wireless adapters to run a keyboard and mouse causes the dedicated PSU with micro USB to still bring up a low voltage warning little yellow lightning bolt on the screen.
HOWEVER! a single 18650 3.7V runs my retro pi setup happily without any warnings. Only when I turn on the audio will it briefly show the lightning bolt due to the dip it creates when turning it on. And it will run for about an hour.
A shorted out 18650 = +- 20A so its VERY capable.
I don't think the issue is the 5.1V as such. When you connect a load to a power ource depending on how much current it's drawing it will cause a voltage drop.
See this.
https://www.robotics.org.za/AF1903?search=boost , It will boost anything from 1.8V and up to 5.2V, check out the link and read the product description. The extra 0.2V compensates for the voltage drop.
So to answer the question. It all depends what you are running on the PI and what else it's powering via the headers and USB ports.
I'm using the mentioned PCB along with a Lithium charger to power my PiGRRL running retro pi.



The Pi has always been sensitive when it comes to voltage.
Besides the PI 4 that I have posted earlier on using the 3D printed enclosure. I also have a Pi2B, connected to a 3.5" adafruit LCD, with a 3W audio amplifier running retro pi. Running retro game emulator on a PI2 most certainly is a good way to punish the CPU and draw more current. Add 3.5" LCD and an Audio amplifier and some Wireless adapters to run a keyboard and mouse causes the dedicated PSU with micro USB to still bring up a low voltage warning little yellow lightning bolt on the screen.
HOWEVER! a single 18650 3.7V runs my retro pi setup happily without any warnings. Only when I turn on the audio will it briefly show the lightning bolt due to the dip it creates when turning it on. And it will run for about an hour.
A shorted out 18650 = +- 20A so its VERY capable.
I don't think the issue is the 5.1V as such. When you connect a load to a power ource depending on how much current it's drawing it will cause a voltage drop.
See this.
https://www.robotics.org.za/AF1903?search=boost , It will boost anything from 1.8V and up to 5.2V, check out the link and read the product description. The extra 0.2V compensates for the voltage drop.
So to answer the question. It all depends what you are running on the PI and what else it's powering via the headers and USB ports.
I'm using the mentioned PCB along with a Lithium charger to power my PiGRRL running retro pi.



