Parties create consensus and help government work better
Have you ever tried to order pizza for a group of 20 people? Now imagine trying with 200 people. The party system, when it works well, makes it easier for governments to make decisions and pass laws. Rather than having to deal with dozens, if not hundreds, of individual views, proposals, amendments and demands, they only have to deal with a few - those of the parties, all of whose members vote together as a bloc. It still means negotiation, consensus and debate, but it means the process doesn’t require getting so many people to agree, which might be impossible without parties to guide them.
Parties train politicians
Parties have many members and officials within them, and helping to run and manage a party can be a formative step in someone’s political career. Many politicians come from the ranks of party officials or staffers. The argument goes that this experience helps people become better politicians - making deals, making connections, learning how government works, and learning how to communicate ideas.