The Rio Grande is only a few inches deep for several hundred miles and there would be no reason to pick out that area to cross with all those gringos watching from their RVs.
Go, enjoy the Big Bend NP. It's really a neat place to stay for a couple days to refresh after a long drive. You can wave at an occasional Mexican villager up on the hillside across the river where there's a small village. And hike up and down the river bank. Or even wade across in places. There's a wildlife marsh area there too (snakes!) with a wooden bridge crossing it.