elveax:
Aren't those the reasons anyone chooses a Li-Ion?
They are part of the reason.
But it is also necessary to consider what is the best (cheapest, smallest, least amount of effort ???) way to provide the voltage(s) that are needed by the project.
One option might be 3 x AAA cells with a tap taken off 2 of them (3v) to power the ESP8266 and the full 4.5v for the other stuff. Don't underestimate the convenience of just replacing alkaline cells when they are depleted. No charger needed. No fire risk. No down time waiting for them to recharge.
Or a 2S Lithium battery with a suitable regulator.
How big physically is the Li-Ion cell you are thinking of using?
...R