Can it charge batteries without a diode? Is the problem that was in the DP8xx series fixed?
It is not a problem. Laboratory PSU is not battery charger.
To charge batteries use charger. They are much cheaper too.
Being able to operate with batteries attached is actually quite helpful for testing and debugging certain scenarios.
Nobody is picking up lab PSUs just to charge batteries, however it is handy when you have a unique battery or scenario that won't play nice with any of the chargers you have lying around.