Over the years I have been licensed by 3 different organizations and am currently ordained in another organization. In the state of Ohio, a person cannot perform weddings without a certificate from the state and that certificate from the state is only obtainable if you are licensed/ordained by a recognized religious organization. Local churches can legally license/ordain ministers and the state will recognize that.
Recently a friend and I made a hospital call. Because the person we wanted to visit was in the ICU and there were restricted visiting hours we were denied access. When I told the person I had a clergy card and showed her my annual fellowship card, she checked it against my driver's license and since it was the same name on both and since I sorta looked like the picture on the driver's license, she let me in to pray for the person. My friend was not allowed in even though I told her that he was with me. She just said, "It doesn't work that way."
In order to have a contact visit (person to person, not by phone while you see each other through a window) with someone in a county jail you have to have an official clergy card. The only card accepted is one issued by the Cincinnati Coalition of Christian Communions and the only way to get that is to show them your authorization from the state to perform marriages. They will not just accept an annual fellowship card from an organization.
So, in order to perform weddings and to visit someone in jail a document from the state is required and that document is only issued when you apply for it and send in a copy of your ordination/license. An annual fellowship card is required to make some hospital visits. These are a couple of reasons for being licensed/ordained by a recognized organization. This may vary from state to state.
In the first century church it seems they issued a letter of recommendation that a minister could take with him/her to assemblies where he or she was not known. I think this is what is spoken of in Romans 16:1-2
and 2 Corinthians 3:1
Just like we need a license to drive, cut hair, sell real estate, etc. in some states, we need a license to perform some ministerial duties. In my opinion, this is just rendering unto Caesar...