Coincidentally I had time in the workshop last night to do exactly this, this is how I learn and satisfy my curiosity!

Spolier alert - results matched widely published theory, I conclude that people not concerned about this have been fooled by built in protection or bad experimental method or just got lucky

I used a Model SCT-013-000 CT, datasheet here. There are variants with built in burden, my ones don't have this, i opened it and it only has a zener or TVS of some kind across the coil on a small PCB. I couldn't read the voltage marking but on a lab power supply with current limit it seemed to start clamping in either polarity at around 10-11Vdc.

CT is 100A rated, I used a resistive fan heater that pulls 10A and put multiple turns of the phase wire through the CT. Was difficult to fit 10 turns so i had to stop at 8 but that's good anyway, we are not exceeding the CT 100A limit.

Simple setup - run the heater, check the CT output voltage with true RMS Fluke 77 meter, record as below. Resistors were what I have in my kit so there are some jumps in value.

Brden R output V
4R7 0.21 V
10R 0.46 V
47 Ω 2.21 V
220 Ω 10.85 V
470 Ω 22.0 V
1k Ω 48.5 V I stopped here, I think the point is proven, 1k is way closer to open circuit than the normal CT burden and frankly i was getting nervous even though it's only <50V no need to go more!

So I can see open circuit going over 50V without the protection diode - not good, I think I will believe all the textbooks and manufacturer datasheets!

Was good to see for myself though, so thanks to all for making me question this, a great result!

You have nearly proven what was said.
"At some point it saturates"
You are way off saturation , hence voltage increases with current .

 

According to this datasheet the TS's device has a 9.2V bidirectional zener across the output terminals.

As in my comment above:

i opened it and it only has a zener or TVS of some kind across the coil on a small PCB. I couldn't read the voltage marking but on a lab power supply with current limit it seemed to start clamping in either polarity at around 10-11Vdc.

But since I measured with a lab power supply by turning it up slowly and looking for current to suddenly go up, I totally believe it's a 9.2V part but this wasn't the measurement I was interested in so I wasn't precise.

EDIT - Oh wait maybe you mean why didn't that diode clamp the voltage - I removed it. I could have made that clearer ;-)

 

Most likely it is a only silicon suppressor, similar to the PKxxx-CA devices, rated for intermittent voltage suppression, not for steady state operation.
Which means that under a constant overvoltage it may have been damaged.

EDIT: read the TS last post. That explains it.