NiMH and NiCad batteries do have some useful properties. We still use Lead Acid too, despite it begin a truly awful battery in terms of energy density and based on fairly ancient designs because it's incredibly robust against environmental changes, can delivery incredibly high currents and don't care about how to charge them; you can comfortable load them up by plugging them into a 14.4V supply.
NiCad for example is great for low temperature environments and they can deliver almost 100% of their capacity at the maximum rated discharge. They are essentially lead-acid with a tad more energy density and being very sensitive about how they're charged.
NiMH don't have that great of a capacity at maximum rated discharge but they do have a very very low internal resistance while still (almost) matching Lithium batteries in energy density. Additionally, they are almost perfectly constant voltage until discharged, making them suitable for applications where you might not want a complicated voltage controller.
Lithium is actually a fairly difficult cell. Drawing maximum discharge will reduce capacity, they don't like shocks or extreme temperatures and their voltage stability is meh at best. They also heat up a lot when charging or discharging, making cooling circuits required in some scenarios. They do have extraordinary energy density though.
Don't discount other battery types; battery chemistry dictates the behaviour of the battery under load scenarios, Lithium batteries aren't always the answer.