From experiment, we have determined that simply pumping kinetic energy into something will only accelerate it asymptoticly close to the speed of light, yes, but I don't think that directly addresses the issue of causality. Right now I believe the discussion is on the level of "depending on where you observe a series of interactions, if FTL is possible then the effect would precede the cause". Most of the causality violations I see in the examples seem to be an artifact of 'what is observed is what happened' that is to say that it assumes light to be the fastest thing so when the light from events reach an observer it is assumed that the order of events observed was the order in which they happened even if some of those events are FTL in nature.
I actually just reread your bomb example. if the triggering action was the reception of the bomb by the FTL radio, then in what reference frame would the bomb exploding precede the detection of the FTL signal?