I was surprised that this didn't work already, since aren't web panels just web pages, and aren't web pages subject to the state of "Lazy Load Restored Tabs"? But if that's unchecked, web panels are still in the lazy load state (i.e. not loaded).
Sure, these aren't tabs, exactly, but it's a distinction without much of a difference. Ideally, I guess, there should be a separate "Lazy Load Restored Web Panels" option for more versatility, but in the meantime it would have been nice if the existing setting pertained to web panels.