There is far more involved here. Genetic drift and other factors play a part also. Unfortunately I start roaming into territory that is outside of my specialty and formal education. Astro/space is my expertise. Hopefully some of the Biologists/geologists will chime in. :)
The random mutagenesis model strikes me as rolling dice. Now, maybe time is sufficient to get enough rolls to come up with new species... but look at all the species that have either existed or currently exist... that's rolling a lot of sevens.
Where I think evolution overreaches in in the presumption that we have a good handle on the mechanism for it. Maybe it's random, but I don't see how that's confirmed in the time frames we've been observing living species scientifically.