Paul writes to the Romans urging them to present their bodies as living sacrifices because of the mercies they have been given by God. This is the essence of what Christian living means - to offer our whole selves with no reservation for the glory of the One who offered himself for us. Instead of thinking highly and only of ourselves, Paul teaches that we are to instead consider the part that each member has been given in the body and the faith that the Lord has apportioned to each. Each member is to use their gifts to serve the rest of the body. All of this: serving the body, loving without hypocrisy, showing honour to one another - is all to be done in service to the Lord. Paul makes this same point in Ephesians 6; we serve one another to serve the Lord.
We don't just serve because stuff needs to get done. Our serve teams are not just necessary evils because a church is an organization that needs people doing something in order to function. Our serve teams are not even primarily to provide a good or a service that supports the Sunday gathering. Serve teams are first and foremost about worshiping the Lord by offering ourselves as living sacrifices. After that, they are about loving one another and building up the body of faith. The service rendered is subservient to these primary goals. Therefore, let us commit ourselves to these things and do them with all generosity, diligence, and cheerfulness!