Why is trade necessary? Is it because the commune would not be able to produce everything it needs and wants?
Correct. It's wants would exceed what it can produce. It can trade the excess of what it produces for other goods and services.
What if it can cover all needs and good enough portion of the wants?
Self sufficiency is difficult at a commune level. Just access to healthcare is a need.
We can see this already in real world. Don't even worry about the commune aspect. A less developed country has lower access to healthcare, education, etc. To develop they have to have something valuable to trade.
Biden's team? Do the Blue Jays give tips to the Yankees now?