No Targaryen Was Going to Rule Again
Both Daenerys and John Snow were huge red herrings. House Targaryen was completely overthrown and driven out of Westeros and for that reason neither Daenerys nor John Snow had a legitimate claim to the Iron Throne. Nobody in Westeros wanted a return to Targaryen rule and since there was no respect or love for that house, the only way Daenerys could rule Westeros was through death and fear. It's possible that John Snow could have had some support, but only as Ned Starks bastard. His true Targaryen lineage would have to remain a closely guarded secret.