First of all, there is no such thing as a 7.4v battery, only 7.4v battery packs made from two 3.7v cells hooked up in series. In theory, if you have two batteries that are half the size you have half as many mAh (milli-ampere hours). So if you take those two batteries and hook them up in series or parallel, you still have exactly the same amount of energy. (When you hook them up in series you get twice the voltage, when you hook them up in parallel you get twice the amount of amps, either way you have the same amount of total energy.) In practice though, smaller cells end up using more (proportionally) for casings, which means less power overall. 18650 batteries come in sizes up to about 3500mAh, but the biggest 18350 battery I can find right now is only 1400mAh. In addition to all this, battery packs require a little extra electronics to make sure the cells stay balanced, but that’s pretty minor.
So, 7.4v batteries don’t give us more power, but are they easier to use?
The answer is a resounding maybe.
It is easy to drop voltage with a linear regulator. A single component can reduce the voltage from 7.4v to 5v, or to whatever voltage we need. However, using linear regulators is not very efficient. The “dropped” voltage doesn’t just magically disappear, it still sucks up battery power, and it produces heat. Let’s say we need 10A @ 5V (a neopixel strip), and we want to use a linear regulator and a 7.4v battery pack to do it. We would need to “drop” 2.4 volts. 2.4v * 10A = 24W. So our linear regulator would give off 24 watts of heat. That’s not cool. (pun intended)
If we leave “easy to use” behind, we can use a buck regulator to regulate the power instead. Buck regulators use a coil to transform the voltage, and gets around ohms and watts law by oscillating back and forth between voltages. A buck regulator might be as much as 98% efficient, meaning that we’re now only producing half a watt of heat rather than 24 watts, much better! Unfortunately, a buck regulator capable of producing 10A requires fairly large components to build and would not easily fit on something as small as a proffieboard.
Now, if I was building a board who’s only purpose was to drive a tri-cree, I might still go for the buck regulator solution, because ideally, powerful LEDs should be driven by a constant-current regulator, which is really just a buck or boost regulator with a feedback loop that controls the voltage in a way that gives you the right amount of current. Most tri-cree are made for 1A, so the size of the components wouldn’t be quite so big.
Ok, but what if we had neopixel strips that can run on 7.4 volts?
Such things actually exists. The 12v strips can run on anything from 6 to 12 volts. However, they use linear regulators internally, so we’re back to being wasteful. In fact, the 5v strips also use linear regulators internally, and the LEDS themselves don’t need the full voltage. Anything over ~3.5 volts doesn’t make the LEDs brighter, just warmer.
Basically, what it comes down to is that 7.4v is too much, and reducing it is either complicated, wasteful, or both. Now, proffieboards do have voltage conversion on it. It uses a boost converter (which is the opposite of a buck converter, because it raises the voltage rather than lowering it.) to convert battery voltage to 5v. The 5v is only used to drive the amplifier though, so it doesn’t need more than about an amp most of the time. The booster used on the proffieboard is rated for about 2A. So we still have some of the complication of voltage conversion on the board, but it’s workable because it’s only for the amplifier. We could actually skip all the voltage conversion and feed the battery voltage directly into the amplifier, but we would end up with a 1.6W amplifier instead of a 3W amplifier. (In fact, this is exactly what I do to reduce the size of the Proffieboard M2)