I would also add point 3.5 which explains that there has been a historic transition (Electroweak Symmetry Breaking) where particles which were massless and trav

I would also add point 3.5 which explains that there has been a historic transition (Electroweak Symmetry Breaking) where particles which were massless and travelling at the speed of light before, slowed down and attained mass due to the Higgs field condensing. As the energy that was released back then due to this transition had to be finite, the Lorentz factor argument about infinite energy can't be entirely accurate: if the transition works in one way without involving infinite energy, it should surely work in the other way too (otherwise energy conservation would be violated).