OK so we can calculate instead of "it's OK, it's OK" handwaving.
Assuming TPS65265
* high-side switch resistance typical 39mOhm, no MAX given, let's assume 50mOhm
* This IC doesn't seem to have an arbitrarily low maximum duty cycle, so it's only limited by bootstrap cap charging time; datasheet is not helpful, so let's assume maximum duty = 98%
At V_out=12V, 98% duty cycle, 4A I_out, Vin must be at least (12V+4A*0.050Ohm) / 0.98 = 12.45V.
12.45V/4 cells = 3.11V/cell
"battery can handle 5A" vs. actual input current of 4A, battery would run at 80% rated maximum current. Now without knowing the exact battery, let's look at some random li-ion cell data, let's pick the good old Samsung 29E from lygte-info; this cell represents quite typical COTS NCA chemistry from a decade ago.
https://lygte-info.dk/review/batteries2012/Samsung%20INR18650-29E%202900mAh%20(Blue)%20UK.htmlMaximum rated current is 8.25A, out of which 80% would be 6.6A, so let's look at the closest discharge curve, 7A curve (blue) of the worst of the two specimen,
At 3.11V/cell, energy is 7Wh. Alternatively, at manufacturer-specified cutoff voltage of 2.8V, energy is 8.8Wh. Available energy at 3.1V cutoff is therefore 79.5%.
So once we done an
actual calculation, even a napkin one, with fair assumptions, we instantly see how "no capacity loss" or "just 5-10%" falls apart. Now I admit there are quite some many assumptions; maybe OP does not mean absolute maximum cell current but some more conservative rating.
On the other hand, if the OP has
any intention to run this at cold ambient - doesn't need to be Siberia-tier weather, just something like +5degC does the trick already - voltage sag of the cells explodes. Same happens when the cells age. End-of-life is usually defined as ESR rise of +100%, meaning voltage sag
doubles. These implications mean that 3.1V cutoff in some totally realistic conditions means losing
more than half of available energy. You don't want to make such compromise willy-nilly; instead, do educated choice.
Really, I say this again: all assumptions about li-ion cells being "fully discharged" at cutoffs > 3V (some say 3, some say 3.3V, most ridiculous claims say 3.5V) are valid
only in low discharge current applications. When the designer specifically says "maximum power" - and here it doesn't matter if it's really absolute maximum, or some kind of recommended long term maximum -, such assumptions should fly out of window that very second. More careful analysis is needed.
This is not limited to li-ion design; alkaline cells share the same tendency of increasing ESR loss near the end, or at cold, so that open-circuit voltage is meaningless. Gadgets that die too early and leave unused battery capacity exist, and people use stuff like Batterizer / build their own Joule thief circuits to make them work. I suggest, don't make that mistake to begin with; design your thing (commercial or hobby) to run down to 0%, or maybe 10% is acceptable, over all intended operating conditions. Something which you
feel is 5% but could in reality be 50% is not acceptable.