Why does a democracy have to involve parties among their members of parliament?
I'm not even sure what you're trying to ask here.

Democracy is putting power in the hands of the people. If the people are unhappy with the government, they can be removed from office. Accountability. As such, policy tends to reflect the will of the people. At least it should. That isn't flawless in the UK, but the UK voter can influence UK government policy a great deal more than EU citizens can influence EU policy.

Parties are important because that's how majorities are formed. Majorities are important because that's how governments work in democracies. MPs vote on issues, and laws can be passed by parties with a majority. We entrust the majority party with this responsibility. and if they fail to live up to that responsibility, they get removed from office at the next opportunity. Or sooner if there's enough noise, forcing a government to resign, triggering an election.

No such process is possible in the EU. Thus, it is not, in my eyes, a true democracy. There is no accountability.