I guess I need some clarification. Power is measured in watts (volt-amps). While some power is burned across resistor setting a 1mA bias current result in roughly 20x less power consumption that running the chain at 20mA with no resistor. So your battery actually runs longer. It’s actually also for safety because if one of the LED’s shorts the current draw will increase dramatically without the resistor. The resistance across a PN junction (LED) is in the mOhm to single ohm range versus that fixed resistor so for the resistor there it will be a lot gentler on the battery and likely reduce the change of operating the other LED’s beyond their operating max of 20mA.
I’d love to meet you in the makerspace and talk through these things. But in summary if we can lower the operating current per chain with a resistor it actually improves the power draw overall.
Edit:
To further clarify. Adding a resistor to the chain gives you a set resistance to baseline your current per chain off of. Using parasitic resistances is generally not ideal due to the fact semiconductor variation often has +/- 20% absolute tolerance. By adding a resistor that’s several orders of magnitude larger you eliminate this variation and thus guarantee the current per branch is roughly equal.
The other benefit is if I add a resistor and clamp current down to 1mA I can now add 19 additional chains of LED’s. Because 1*20 = original 20mA.