The chemistry defines the voltage of the battery. Lithium operates anywhere from 3V to 4.45V or 1.5V.

The biggest challenge between chemistries is going to be energy density compared to other types, cost and sometimes weight and size.

Lithium is becoming battery leader in terms of chemistry, because it has a higher energy density, lower weight and can come in many form factors. The biggest downside is cost.

Alkaline has the benefit that it's low cost, decent for most cases in terms of size & weight ratios. NiCDs are heavier.

Energizer makes lithium AA/AAA that are 1.5V. The biggest benefit over alkaline is that those lithium batteries have longer runtime (also work better in cold). However, the lithium batteries are more expensive and you could probably buy more alkalines for the same cost.

It's worth mentioning that non-rechargables typically hold charge longer than their rechargable counterparts, the benefit of rechargable is that you shouldn't have to recycle rechargables away after it discharges. This means on one charge cycle, you'll have to charge the rechargable before the non-rechargable. Non-rechargables are quick to replace but you have to buy more over time.

With this in consideration cheap electronics typically come with alkalines AA/AAA because it's cost effective, provides the needed power and decent runtime and they don't care too much about you needing to replace the battery when it's discharged.