I'll confess I am a "ripper" too. I like to take an extra wide seam when piecing long lengths of backing fabric (1/2 inch) so don't usually have to trim off the distorted edges. For borders I just make sure to allow an extra 1/4 to 1/2 inch or so in width of torn strips, then I get rid of the first 2 or 3 loose threads on the edges of the strips I've torn. I find good quality fabric is easy to tear and doesn't usually even need trimming.