non-pastors baptizing

I would assume it's largely a residual effect in church evolutionary (begging your pardon) history. Specifically, it's a remainder of the concept of priestly power. The Roman church still adheres to its heirarchical structure, one meaning of which is that only those ordained by The Church can perform certain rites, or "sacraments-- baptism, eucharist, marriage, unction and the rest. Separating from the Roman church obviously meant that line of aurthority had to be replaced, and at first it was mostly replaced by a similar line within the new denominations, some of which retained the priestly authority concept; but extending the reformation further, some abolished such an idea as priests, but retained clergy as 'ministers' only [they served the congregations, but were not 'go-betweens' of the masses and God], but still only 'authorized' the ministers for certain acts similar to the Catholic sacraments-- baptism, communion, marriage, et al.

In recent generations we have seen these continuing residual effects being lessened further... the church building [structure] is not a 'holy' place to the exclusion of any place people gather for worship, Sunday may still be the primary day of meeting, but it's not a quasi-sabbath in which people are not to cook, wash, or make their beds, etc.; and, though many may dislike it, the/a minister is not a holy man or the "Lord's Hand" who has unquestioned authority-- it's this that is still clung to in many settings; that only the man with ' the authority'-- the education, the ordination, the one not called by his first name without a title in front of it, can do the baptisms, weddings, funerals, communion... Basically it's just history and tradition.