[...] A lab PSU is the wrong tool for battery charging [...]
Is that totally fair? - a lab PSU is a general purpose source of power that shouldn't really care what you use it for (within reason!). A battery charger is an application specific device. So, I would accept that the charger is "better"... but surely I should feel OK about connecting anything I like to my lab power supply that isn't directly insane?
For example, the other day I was measuring the internal resistance of a bunch of NiMH cells. My battery charger was not able to do this... so I used my ancient lab power supply in constant current mode and measured the difference in voltage drop between two currents, differing by 200mA. So, connecting a battery to the supply is a possible use case even if you are not charging it...
Also, consider the use case of charging a supercap, or even a regular capacitor (massive capacitor bank in an audio amplifier, for example) and subsequently decide to lower the voltage...
Overall, it seems preferable to me that a lab supply is able to deal with these kinds of real world scenarios without the risk of self destruction. Granted, a crowbar is always going to be an issue and probably should not be used without a fuse... but that could also be baked in.