Thanks. May I ask how they were used in the past? I know this supply is older, so back in the days, how did they avoid this "problem"?
Is there maybe a circuit I can build so that it works like a modern lab PSU? I don't know how modern PSU avoid this problem, but I guess that you can build something around it or?
A series resistor would indeed limit the inrush current. Is there another way to do a "soft start"?
We used these supplies in my undergrad labs. I've also used these supplies in semi-permanent test setups as a "system supply" where a board/device needs power. I've only used them as constant-voltage sources. I wouldn't normally use them in a situation where I'm constantly tweaking output parameters (I'd use something digitally-controlled, instead). The CC limit is mostly just to prevent the DUT from catching on fire or fuses blowing. Anything with a large output capacitor won't work well as constant-current source with respect to load transients.
Most modern supplies will have an "output-enable" button, so wouldn't need to be powered off to disable the output. Also supplies designed for CC operation will have a much smaller output capacitor.
As millerj mentioned, one solution is to turn down the voltage to zero prior to attaching the load.
I think you could add a front-panel toggle-switch to set the output to 0V. I'm not able to quickly visualize all the feedback loops, so I could be opposite and it would set the output to max voltage. It also could create some transient ringing during use, as I'm sure they didn't design the circuit to slew very quickly. See the attached drawing.
Anyway... the optimal solution probably is to add some series resistance to your testbench, and then use a separate DVM to get the LED forward voltage.