Intelligence is no solution in itself, it is merely an effective searchlight for unknown unknowns and who knows that the brightness of the light increases proportionally with the distance between unknown unknowns? To enable an intelligence explosion the light would have to reach out much farther with each increase in intelligence than the increase of the distance between unknown unknowns. I just don’t see that to be a reasonable assumption.

We do have some data on historical increases in intelligence due to organic and cultural evolution. There's the fossil record of brain sizes, plus data like the Flynn effect. The process has been super-exponential. The intelligence eplosion has been going on for about 500 million years so far. As Moravec puts it:

The largest nervous systems doubled in size about every fifteen million years since the Cambrian explosion 550 million years ago. Robot controllers double in complexity (processing power) every year or two.

Machine intelligence looks set to be a straightforwards continuation of this long and well-established trend towards bigger brains in the brainiest creatures.