Even if Henry doesn't want to get remarried and is happy being pious and ineffective there'd likely be pressure from the anti-York clique (Beauforts, de la Poles etc.). However, if you kill Margaret early enough and thereby remove her hostility to York, then York might be in better standing with the Henrician regime and remove some of his disaffection- he might talk his way out of going to Ireland, regain French appointments etc.
Also, if Margaret dies really quickly what does that mean for Maine/Anjou, would it void the treaty that said the English would hand it over? Does that mean France invades? Because not limply handing over English conquests without a fight mollifies York and those dissatisfied with the war effort (and maybe they don't despise Somerset and Suffolk quite so much).