Good human logic, but forgive me for choosing God's word over your reasoning. Notice how the Lutheran position on the Lord's Supper uses biblical evidence, but your position uses human logic? I know which one I'd rather believe.
It's not human logic though, it's Scripture.
"While they were eating, Jesus took
bread", Matthew 26:26. How else can that be interpreted? They were celebrating a Passover meal together, Matthew 26:18 - the meal involved lamb, bread without yeast, herbs etc, which all symbolised and reminded them of the time when God delivered them from Egypt.
The bread made without yeast was because they were in a hurry and didn't have time to wait for it to rise, although they later also had to remove all yeast from their homes. The lamb was the lamb that was killed and its blood put on the doorpost which saved them from literal death.
After supper, Jesus took the cup; in Matthew Jesus says it is the fruit of the vine, Matthew 26:29.
Yes, Jesus is the bread of life, John 6:35.
Yes, Jesus is the true vine, John 15:1
Yes, Christ is our Passover Lamb, 1 Corinthians 5:7, and in this, and other verses, yeast represents sin which we are to get rid of.
But all these are metaphorical. Jesus was not literally a piece of bread, a cracker, a plant or a fluffy sheep; he was a man and also God. He did not literally cut off a finger, pass it round the table, let the blood drip into a cup and make them drink it.
When we eat and drink at communion we are, in some way, taking Christ, the bread of life and true vine, into our hearts and lives. We are remembering his death, honouring him and commemorating that he, the source and substance of life, gave his own life for us so that we could be reconciled to God and have eternal life.
That is what is important; that we celebrate Jesus' death, receive him and give thanks to God for what he did for us.