I'm not sure I agree with this. I think we can make an argument from Scripture, particularly the Great Commission, that all disciples are authorized to baptize. Where do we find in Scripture you must be authorized by the local church?
IMO, it’s more of a politeness thing than a biiblical thing. Unless someone’s Church of Christ, there’s no need to rush the Baptism, because most Baptists don’t believe that baptism is needed for salvation.
In addition, baptism is considered a form of an entrance ritual. (Please excuse the clumsiness of my words. I might not be using the right jargon.) After the Baptism, the person is considered a new member of that particular local church. Leaving the local church out of this doesn’t seem right. In addition, it would make sense then that a member of that local church do the baptizing.
In addition, Baptists traditionally baptize in public. It’s what got the early Baptists murdered by the Reformed Church. There should be witnesses to the Baptism who know what is going on.
Now some of this, like the public Baptism of followers, is in the Bible. (Acts 10:47 - notice Peter also asks if anyone objects.) Other parts are simply submission to the local authority of the elders of your local church. (Which even Paul did when he went back to Jerusalem. Act 21:23)
Of course, if you don’t like the local churches, you can always start a new one. Although, I wouldn’t do so over petty matters.