Both concepts are taught in Scripture, local and universal. I am a strong believer in the local church in carrying out God's work on this earth. The universal church is an abstract concept on this earth before eternity. The universal church (all believers) never helped the sick, poor, or needy. The universal never sponsered a missionary in foreign lands. It never went on visitation. It never took up an offering. It never conducted a worship service. It never administered the Lords Supper or Baptism. It never chose deacons, elders or called a pastor. It never offered praise and honor to the Lord. In other words, the universal church here on earth is a useless entity. In eternity is another matter.
Catholics worry about a universal visible church, and we see the results of that. Protestants refashioned the model to use a universal, invisible church, more science fiction. We are Baptists. Our churches are local, visible churchs, designed to carry out the work of the Lord. The churches in the NT are clearly local churches. All having a hierarchy does is waste money, and put levels of government between a lost and dying world and the local NT church. Presbyters, bishops, cardinals and other hierarchy officials of various stripes in essence take of space and waste our food supply while accomplishing nothing for the Lord.
Even when Catholics refer to their "one true church" they in reality do not believe in a universal church as Scripture speaks of. The universal church is all believers from start to end. Catholics conceive the universal church as a roll call of their members, with others headed for the Lake of Fire. Protestants hold to a "universal, invisible" church, or as they put it, the holy catholic church, communion of saints, etc. Again, they fail to give any function of the true universal church outside their own denominational lines.
Revelation speaks of and gives a vivid picture of the universal church, as we all stand before the Lord. The bride and all redeemed come out of the universal church. This is future tense. How does a universal church, here and now, on this earth, (you know, blue sky, green trees, people walking around) carrying out the last chapter of Matthew?
I do agree the point made by several that the church was added to daily, and not voted on. That is another thread about church government. Surfice to say, it says daily, not after some period of indoctrination, communicants class, examination, or other such nonsense probation period.
We are here to tell others about Jesus. We are not here to create levels of government, wear stupid looking costumes and wave pots with smoke coming out. We are not here to waste the Lord's money, as it is all His. We are not here to make power grabs within a local church, or argue over the thickness of the toilet paper.
Until you die, the local church is God's instrument for us to accomplish His work.