GameBoy Pocket Backlight doesn't work with Ezflash JR

That's typical on modded systems

 

When your power delivery is trash, stuff like this happens. Your GB Pocket needs a strong battery to work on a modded Gameboy with a flash cart. This is why GB Pockets are the only model I don't fuck with, they're too finicky and don't have any good battery mods.

 

Get Enloop batteries or UltraCell Plus NiZn 1.6v AAA - 1150mWh High Voltage rechargeables . Should get you 4hrs of playtime.

 

NiMh batteries are only 1.2V, try with some alkaline AAs or as @B.B.Link suggested, get some NiZn, just beware they need a special charger, and the battery life is maybe not as good as high end NiMhs. You can also get 1.5V li-ion AAs (they have a tiny li-ion cell inside with a voltage regulator to change 1.5 to 4.2 and vice versa) but the battery life is kinda poor because so much of the internal space is taken up by the voltage regulator circuitry. Those also need a special charger but often they come with some sort of USB charger.
I use DMG myself and thankfully the Ezflash Jr works fine on that.

 

Why can't they just make NiMh batteries at 1.5v? Is it possible? Not possible?

 

Not possible I think. Just like making AA batteries at different voltages isn't possible (9V batteries are just 6 AAAA cells in series... if you open one up you'll see)
The specific chemistry is what decides the voltage. For example, li-ion/lipo batteries are always 3.7 or 3.8V but LiFePo4 (similar, yet different) are 3.2V.

 

I've been wondering why there's no "TRUE" 5v and 6v batteries out on the market. It's pretty annoying, to say the least. It's like battery engineers and electronics engineers just aren't talking.

 

It's hard to come up with new battery chemistries. There's constantly research done on it, but most of it isn't viable for mass production. They kind of don't get to pick the voltage, they just have to work with what the battery chemistry naturally produces.
You could make a battery that's connected in series internally to get a higher voltage (and there are lipo cells that do so), but it will always be a multiple of the 3.7v nominal voltage (in the case of lipo), so it doesn't really give you much control.

 

I always use 18650's for my larger projects, and can kind of control their output with a DC to DC stepdown circuit to get 5.2v out of them to power a Pi 3 or Pi 4. (2 connected in series)