Dick,
More relevant to Shakespeare than getting your head removed would have been earning his bread. He got precious little from acting and I don't think he got much published in his own time. Writers got their income from the patronage of royalty and nobility. So it was the 'sucking up' factor rather than the fear factor that encouraged Shakespeare to toe the line on the history plays. As well as DickIII sucking up to Liz, Macbeth was completely altered to suck up to JasI.