I don't always quilt in my borders and they seem to wear just fine. I have one I use as a throw and since the dogs snuggle in it too it's washed very frequently and no problems at all with batting shifting. We probably do launder things more often than in days of yore but batting is a lot more stable now too, so I think that compensates.
If you do ties, think about the loooong expanses with no ties! If you were tying that quilt you could very well have had ties along the edge of the border and not in the border at all and it would have been fine.
The way my gran taught me (and she tied all her quilts) is that if you need a tie every 6 inches that means if you go 6 inches out from your first tie and use that measurement to draw an imaginary circle (so a 12-inch circle with a tie in the center), you need to put ties on that circle edge; top, bottom, left, right. Keep that up until the entire quilt is covered.
If you have a quilt tied like that, or draw up one in your imagination or on a piece of paper, you can see there are long stretches in each direction with nothing securing it. My gran made ALL of her quilts that way, and they all have survived wonderfully. The bindings wear out and some ties go missing over the years but I've never had one where the batting shifted.