There is nothing really logical in their favour as compared to modern nose wheel types. Nothing at all
Im confident you're kidding...
But, for those who would take this statement seriously, go fly a nose wheel equipped ski or tundra tire plane, then the equivilent taildragger, and you'll have a much greater appreciation of the virtues of taildraggers.
I'd much rather take a taildragger into rough, or unknown ground, than a nose wheel aircraft.