I've been in an attic many times on a sunny day. The heat in the attic is well above what it is outside. I'm highly skeptical that an unvented attic is going to keep a house cool in summer.

Me too. But have you been in a competently built insulated and unvented attic? The insulation on top makes an enormous difference, to the point that the attic can usually maintain a very pleasant temperature.

While it’s true that the top side of above-attic insulation will be rather warmer than a vented attic on a hot sunny day, insulation on top of your attic also tends to work rather better than ceiling insulation. And there are plenty of other benefits to an unvented, insulated attic.