Loto replied on Youtube. It turns out, you have to hit Stop device button and then, finally, those PC cache thumbnails become available and you can scroll the signal into view. A bit convoluted, but it works. As I understand, that's mostly necessary only for their lower-end models with software triggers because those fail to "focus" the signal into the main view.
Loto also suggested buying one of their models with hardware triggers, but even with a properly focusing trigger you might want to be able to scroll a long signal, and then also you would have to stop the device. I'm not sure why this limitation - why users should be blocked from viewing a cached signal immediately while you are already paused on the trigger anyway.
Well, for now, I can live with that. I wish there was a seamless zooming / panning of the main view instead of the awkward routine "Stop device, click on a thumbnail, and use a scrollbar until the signal is in focus".
Picoscope 7 demo mode feels nice indeed, everything seems intuitive and convenient enough even for a newbie.