I think it came from the charismatic movement as did the music. It was a fad that swept many churches and they forgot to get rid of it. It isn't a baptist thing in particular, it is in many groups.
One morning our pastor just finished some thoughtful comments with, "we too often get tied up with things and people rather than God" then he said, "Let's take a moment to shake everyone's hand!" Now if that isn't a people centered thing I don't know what it is.
As mentioned, it detracts totally from any part of worship that you might have brought to the service thus far.
I have noticed in most churches it replaces getting to know visiters when they come in and leave - get your duty done during the worship time when you don't have to do much but say hi.
We visited one church for quite awhile and during the greeting time it was super friendly, but absolutely no one has taken an interest in us otherwise - We get to worship which is always good :-)
I also suspect that some pastors use it so they have a friendly church without him doing it.
It can be a very effective time, in my mind, - not that it is Biblical in particular - if each person singles out one other person to greet and spend a moment or two with getting to know them. It is especially helpful if a visitor is met with a one on one contact.
Visited a large church once when the pastor had the congregation stand, then he asked the visitors to sit down, then introduced the greeting time. Can you imagine 200 hands coming down at you as you cower in the pew <img src="/forum/images/graemlins/wow1.gif" alt="" />
