> A star "lasts" about 10 billion years, so you'd expect about 1 in 10 billion stars to 'die' each year, but only a tiny proportion (the very largest) go supernova.

This analysis really doesn't work. Star lifespan is inversely correlated to size. A star large enough to just barely go supernova is only going to live for ~100M years, and as they get bigger, the lifespans fall rapidly.

(Why? Because gravity is what provides the pressure for fusion to happen, and so more gravity means fusion happens faster. For large stars, the luminosity is something like the mass to the 3.5th power. Also, convection works less well for larger stars, so as stars grow bigger, ever smaller proportion of the star takes any part in the fusion reactions in the core.)