Managed webclip in Single App permitted mode shows white screen

This is a bit difficult. You're likely running up against the wifi not connecting before the web clip tries to load. There isn't really a way around it.

1. Apple is well versed in always on displays and protecting those displays from damage. This is a very low risk for the customer. If you're using one of the lower end iPad models, or an older higher end model without OLED, the risk is almost non-existent. I've run kiosks for years without burn-in issues.
2. If the web clip isn't loading properly, I would argue that there is a reason to have it turned on.
3. You're saving pennies of power per year. The cost or running an iPad at the maximum kWh rate listed in the US would be about $18 for the year. At the average rate, it would be about $7.50.

All that to say, you're engineering yourself a headache for maybe $10/year savings.

The new app wrapper definitely will help. Because it's an app rather than a web clip, the Single App Mode typically applies at load, then the app loads while the device connects to wifi, and then the app loads the site. A web clip loads while the device connects to wifi, resulting in the white screen you were seeing. Nice workaround!

Is there a reason the devices are turned off at all? Likely your WiFi is not connecting before the web clip attempts to load.

May I know which MDM you are using or what are the configs set from MDM. May be something to do with the way SAM is set up for the web clip.