Re: "onboard computers dramatically shut down the rocket"
Three meters up it becomes engine out. Not shutdown all nine.
Like the Shuttle, Saturn etc.. last seconds are about checking engine performance if all as expected its launch commit, from that point on unless your configuration cant tolerate loss of an engine (aka Orbitals Antares) it goes up to either a bad orbit or to be destroyed for a severely sub-optimal trajectory.
Falcon 9 has up to two engine out capability, though I think more than a single engine out on initial boost, would result in the aforementioned rapid disassembly process.