welcome to the board. i apologise in advance, but that doesn't look like damage due to wear. it looks more like it was chewed on by rodent, or family pet. it's also coarse weave like drapery fabric ...which would not have been uncommon in past decades, and would be prone to fraying with any damage. do you know the history of the quilt? it's age, region of origin? i also would abhore the idea of stitching on binding ...and i especially wouldn't serge it. if you can visit a museum near you with a knowledgeable staff member that is familiar with the care & repair of vintage linens ..that's what i would do. i don't live near a textile or any type of museum that i could get help from. i have also collected vintage & antique lovelies for many years thru our travels around the united states. i am aware that my only child doesn't share my love of these items ..and looking at the 'sold' prices on places like ebay ...i am also aware that the value of collectables/antiques changes frequently according to the latest trends.
therefore ..i've become sorta rogue in my thinking about my treasures. if your quilt were mine, i would do one of several things. my first idea is that i would unstitch all the way around, trim the top back to edge of damage, then turn under and restitch. and yes ...since it was done by hand, i would repair it by hand. you could just do the side where damage, but that might leave it 'unbalanced'. i, personally, would love to see a pic of the full quilt!! it looks like a beautiful vintage print. good luck with your treasure.
additional note: looking at your pic on zoom, i am wondering if perhaps there was i adequate turn under for the knife edge style binding? ..what is the backing?