Funny enough, Washington wasn't a fan of parties. The argument against them is that they encourage lazy voting. Sure, there are advantages in that a party will help summarize a list of policies, but the disadvantage is tribalism. I think in modern day we don't have the same need for policy hinting (what parties give) because every major politician lists all their policies and positions on their campaign websites. 50 years ago this would be a logistical nightmare.

That said, if we adopted something like score or STAR I don't think there would be any problem with parties, nor would they be destroyed. You still get the advantages of pooling resources. Have a strong preference for members of the hippo party? You can donate and campaign for them even while you hash out which candidate best represents the coalition of people at the time. Think the hippo party played dirty and kicked out your favorite candidate Salamander-Gibbon Yack but really don't like the opposing party Tree Trunks? You can still vote your favorite person and not have any determent (system is monotonic). This actually gives less power for the hippo party to determine for you which is your preferred candidate.

Better yet, you get a lot of information! So even if the hippo party's leading candidate wins but you find that Salamander-Gibbon Yack was an extremely close second then the hippo party will have to update their policies (hopefully). By rating, instead of ranking, candidates you have a substantially more expressive ballot and we can data mine and learn from it through this expressiveness. We live in the age of big data and yet in politics we compress data to a point that is almost meaningless.

Cardinal systems won't destroy political parties, but they prevent them from controlling and manipulating the elections.