The luck factor at least in most of the games from 1-8 had at least the possibility of thinking up a strategy to win (Even if there is a possibility of stuff like a chance time deciding the entire game on the final turn) like any other board game. I think alot of the appeal of Mario Party is that it's a board game that's simpler and also more varied (Different maps and all) then Monopoly and without needing to clean up a mess of pieces once the game was over. With the bonus of having (mostly) fun minigames just about every turn.
Luck certainly comes up alot, but much of the early Mario Parties still allowed you to have a free-roam of decisions on where you go, trying to predict where the next star will go if you know someone's going to get it before you, how to prevent other players from getting stars, and winning Mini-games/earning coins to get you items that you personally decide to use whenever you want to try to turn the tide of the game in your favor.
Though to be fair, the experience with Mario Party definitely goes up depending how many local friends you have available. Cause most Mario Party games certainly don't provide too much for someone playing alone. From a single-player perspective I could see that being a knock against the whole series. Though it is called Mario Party for a reason.