Ok, yes, there are wall-warts that do this, mostly bad SMPS designs. Older transformer based wall-warts are either unregulated or have something like an 78xx, so don't have this issue. The majority of SMPS wall warts I've seen so far did exhibit a bit of overshoot on turn on, but are okay otherwise. But yes, of course, there are wall warts around that are horrible in many ways.
I know that Hameg once built a few supplies that had this issue. People complained, they fixed it. And they rightfully complained.
I've worked with a few HPs, mostly older ones, never saw anything like that. Simulated many of their designs (yes, with focus on stability and turn on/off behaviour), built two of them, no spikes. And seriously, this is so simple to avoid completely with a proper design, it's just ridiculous to argue that "this is normal and can't be fixed".
I attached a scope screen grab of my version (different output values and power transistors, otherwise identical) of the E3630A. The design of this supply is used by HP for a long time, for example in the 6236B and a few others. It's one of their two main designs for bench top, pot-controlled supplies. I challenge everyone to point out the spot where I turned the mains on. Output switch was on, volts pot down to zero.
/edit: Note: I generally don't work with SMPS lab supplies on my bench and worked only once with a 19" high power SMPS, so I don't know if my remark that this is easy to fix applies to SMPS as well, however, for linear (at least last stage linear) supplies this is easy to fix. If this should really be common with SMPS lab supplies it's one more argument against them, imho.