I suppose I just don't understand why the Church has a law allowing people to marry within a month
I don’t think it’s that simple. I looked up the canons that Principio mentioned and they had nothing to do with any month time period. So we would all need to read the actual code in context to get more details.
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I could see the only exception of 1 month being applicable to the following scenarios: 1) the couple lives in an anti-catholic country and normal, diocesan churches don’t exist, or are in hiding for persecution, or are spread out and priests aren’t available often (China, Middle East). 2) same issues as above due to war, or other disasters, 3) the couple is on some remote island or mountain place where the church/priest is not close (ie in the Bible Belt), and maybe the couple can’t travel due to family sickness or some other reason. So they can get married, to avoid the occasion of sin, and then find a priest to get blessed later.
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In all other cases, the couple is obligated to present themselves before a diocesan priest (or Trad priest) and the normal preparations, classes and such are required. The only reason the priest/Church makes a couple wait is so She/priest can provide classes and to be a witness that the couple is aware of the sacramental obligations and there is no impediment. But in crisis situations, the couple vowing before God suffices.