Jesus himself instituted baptism
Wrong. Jesus himself never performed a baptism. His 12 apostles weren't baptized by him. Some of them weren't even baptized by John. But Jesus was indeed baptized by John, who performed baptisms in the same fashion the Essenes had been practising for nearly a century already. The passage of Matthew 28:19, 20 (like many sayings attributed to Jesus in this gospel, also in Luke) is most likely a later adition to justify the practice of baptism by the christians. Actually, one of the most well established events of Jesus's life is also one of the things that caused more embarassments to the early christians: the fact that Jesus was baptized by John, thus being his disciple. THIS was an embarassing fact that the early christian writers had to get very creative in order to make it look otherwise. In turn, around those explanations, a whole new theology was then constructed (erm ... invented)