Maybe I'm old and wedded

to our historical ways, but what would really change if all marriage licenses were granted by Legal Zoom instead of by the local state Justice of the Peace?
Except that it might put some Justice of the Peace's out of work?
Lets say that you need your marriage license to prove your marriage to a hospital so you can visit your sick spouse in a hospital that limits visitors to parents and spouses.
And lets say that you are in a LGBT marriage and obtained your marriage license thru Legal Zoom and your spouse is in a hospital.
You bring your Legal Zoom marriage license to the hospital so you can visit your spouse.
Can the hospital refuse to let you visit your spouse because you have a Legal Zoom marriage license?
Can a hospital refuse to let you visit your spouse even if your marriage license was granted by your local state Justice of the Peace?
Or can a hospital refuse to let you visit your spouse no matter who granted the marriage license if you are a LGBT couple and the hospital wants to discriminate against you?
The above may be a clumsy example, but its the best I've been able to think of so far. What I'm trying to get at is if all marriages are now granted as soon as two people (of whatever persuasion) sign their Legal Zoom document, would these two people always be considered to be "married" for all purposes, and there would be no distinction in any court of law or other societal situation?
If so, then how does this limit LGBT marriages? (which I assume to be the purpose behind various religious groups opposition to LGBT marriages). Wouldn't marriage licenses be even easier to obtain using Legal Zoom than what was necessary before when using a local Justice of the Peace? Or would "Legal Zoom" marriage licenses now be considered "second class" and this would allow more institutions an easier path to discriminate against LGBT couples?
Respectfully,
GTsail