"In the same way, baptism is meant as a symbol to show the rest of the world that you're saved."
There's another piece to this analogy. To begin with, it would be expected of anyone seeking God's will to be sure any major given teaching or practice is scriptural, like
"thank you for the analogy, now what is the scriptural basis for baptism in Jesus's name being meant as a symbol to show the rest of the world that were saved?"
To be responsible, we hopefully don't just take somebody's word for it and at least check the Bible to see if it's true. But there's also an assumption made in this analogy that I never hear asked about either.
It is assumed, not stated, that a newly saved person is also expected to hold an event to symbolize or to show the rest of the world that we are saved or what Christ has done for us.
So, in addition to walking as Jesus did 1John 2:6, in addition to preaching the gospel Mark 16:15, in addition to not to disowning but rather confessing Jesus before men Matthew 10:32-33, this analogy now also expects a newly saved person to do something to symbolize or announce to the world that they have been saved. The question deserves to be asked "Does the New Testament expect a just born child of God to hold an event after being saved to let the whole world know, and if so, where is such an expectation written?"
I have never heard this topic addressed by those who verbalize the wedding ring analogy. Nor have I ever heard someone ask about it. Due to the way the analogy is phrased, this expectation is just accepted.
To me, it seems like by design. They don't say, "you are expected to hold an event letting the world know you are saved, and baptism in Jesus's name is that event".
They skip that first part and speak as though it is assumed (without establishing it), "baptism in Jesus's name IS THE event assigned to show the rest of the world that you're saved." It's a great way to get around having to address a non-existent expectation.
It is indicative of a culture that deemphasizes scripture and emphasizes the narrative and reliance on the deliverers of that narrative.
Your thoughts are appreciated.