homemade Wood Router - project failed And almost got me seriously injured- READ DESCR

[Claudio HG]

There is no indication in the video that the shaft actually broke,

If you read carefully at the end of the video you see the shaft is broken. Even the OP confirmed it in a previous comment.
But you have a point about the allen screw fastening (I didn't thought at it at first sight): that certainly induced a vibration (an oscillation of the moment with the fulcrum at the bearing) that made the shaft subject to a pulsed shear/bending force exacerbated by the contact of the bit with wood that, because its veins, induced further variations in the moment.
This could have been coumpounded and potentially resonate, increasing on some instants the peak of said shear force.

About the motor shafts, these are usually thinner in universal motors to reduce instabilities and increase lighweight when they are meant to hold axial forces only. In the industry it is usual to make these shafts with a particular grade of steel (that vary among manufacturers) able to widthstant the axial force despite the reduced section. Also AFAIK often they haden the steel (not as a file, though) at the location where the shaft will be in contact with bearings: I've seen a manufacturer of wiper motors that uses an induction coil to harden the steel where the shaft will mate with bearings.
I am not an expert in metallurgy neither a mechanical engineer, but my experience was that motor's shafts generally are harder that C45 steel and brittler, far less than a file though. So I do not dispute your reasoning about the choice of steel, actually I second: the steel will be likely somewhat around 700-900 MPa, thinner than what it should have been if it were meant to withstand mixed, pulsed forces, and this is a further reason to see it broken when a pulsed shearing force is applied to it.

EDIT: Grammar.