AC to DC power supply - earth ground capacitance on DC output
There's plenty of mains AC powered equipment which behave as yours. They have metallic shield to reduce electromagnetic interference. That shield is connected directly or with a big capacitor to the output which the designer considered to be the signal ground or the voltage ground.

In addition it's connected to the protective earth wire of mains AC input. Finally they have a LC filter in the mains AC wires which has  substantial capacitors connected from the shield to both mains AC wires.

 

If you connect a device like this to unearthed mains AC socket, you will have perfect 50% of the local AC voltage at the output and the shield. A lot of people have destroyed loads of equipment when they were plugging or unplugging devices to other devices without knowing this.

Especially disastrous are attempts to get rid of noise gathering ground loops by breaking somehow the protective earth connection. I have seen several audio systems silenced with this method. Connect or disconnect a cable or cables in a wrong order = kaputt.

Is it poor design? It is poor if one has a reason to assume it will work safely without a connection to the protective earth.