Multiple historical references.
Yes, the plot needed the timelines you've mentioned, and also it had to be the Texas border, pre-fence.
Wouldn't the fence have changed things?*
Then, another reference to history:
Ch V, p 134 (after a shooting).
"There's days I'm in favor of giving the whole damn place back to 'em, the sheriff said.
I hear you, Bell said".
I was feeling a little lost (probably from lack of interest in shootings) at that stage, and I wondered whether the first sheriff wouldn't be Mexican by any chance, and mostly I wondered who "em" was. Bandits? Mexico?
The choice of Eagle Pass as location is important I think, it's one of those cities that straddle the border between Texas and Mexico (as I've just found out from wiki).
The drug traffic and the bad guys like Chigurgh thrive on coming and going bewtween the two countries, and the allusion to giving back the place to Mexico gives us a further historical landmark: a time in the past when the tate of Texas didn't exist and there was only Mexico, so pre-1836.
* Out of curiosity: from what I read, in 2007 the fence through Eagle Pass had still not been built because of a court decision against it.
Does anybody know whether it has been built now?