The correct term is "memory effect", when I used to simply say memory I was finally questioned as to why can't they just build them without memory so I'm careful to note that is just an effect that makes it appear as to have memory
memory effect was pretty much taken care of after the first NiCads used by nasa in satelites.
NiCad's are the most tolerant of being constantly charged but that doesn't mean that a constant trickle charger is a good way to charge them. NiCad would probably be the easiest to put into something that might be left in to charge or have an on consistnet charge cycle like that from a solar or crank charger. NiMH is less tolerant and will go bad in just a couple years if used that way.
Self discharge is also an issue. Batteries sitting around will slowly drain over time and if they get too low polarity reversal can happen resulting in a bad cell in the pack.
To get the best battery life you really need a smart charger and a maintenance schedule. Thats why I don't like products like these, they are treating the batteries in the worst ways possible yet may be relied on in an emergency. many people will pull these kind of deviced out of their emergency kits only to find the batteries have gone bad and can barely hold a charge for longer than the crank is turned.