Nonsense. NiCDs and NiMH batteries love to be discharged. That's the only way to store them for long periods. Don't "reverse charge" cell(s) in a multi-cell battery by discharging it below about 1V/cell though. They can be left to self discharge without damage. A single cell battery can be discharged to zero.
OTOH, lead-acid batteries must never be fully discharged and must be stored with a float charge. Lead-acid batteries are thus better for things like flashlights, UPSs, safety lighting, and such.
Not any more. NiCds may be 20% per month, usually less. NiMH has gotten a lot better too, but it was never as bad as 10% per day.