Great commission applies to all believers, but the laity does not baptize. Why?

I just noticed that while we are told that the great commission applies to all believers in the sense that we are to share the gospel, we don't normally baptize those we help believe. Instead, we bring them to church to be baptized by our clergy. Is there any basis for this practice? Note: If your denomination allows your laity to baptize other people as a normative/regular thing, this question is likely not relevant to you. I would love to hear answers from denominations where clergy would normally administer the sacraments.