Per my understanding, if Mexico signed a safe third country agreement, Central American migrants would no longer be able to cross the U.S.-Mexico border to surrender to U.S. authorities and stay in the country while they await asylum proceedings.
Again, I'm not saying if this policy ultimately benefits the US or not for the reasons you cite or if it will be effective in practice, but it is/was a current demand from the Trump administration that Mexico had historically been opposed.
Exactly, and I don't know if it is beneficial for anyone either. When I brought it up I was speculating, that would be the only "real" thing he could do.
Most likely scenario is both countries pay some lip service to "working together and doing something", nothing actually changes and Trump pretends he won some grand victory.