Aside from using Alt+M on each pair, is there an easier and faster way to merge vertices that share an edge? You’d think this would be an easily accessible feature by now.
I’m not sure I understand your question but if I do, edge collapse could work for you. Try this: select the edge, hit X to spawn the delete menu and choose edge collpase (you can do this very fast by hitting x and the c)
Select a Vert, double hit G to slide it along an edge and then slide it into the Vert you want to merge it into.
I read somewhere (think StackExchange) that using Remove Doubles also merges nearby edges/vertices. This worked for my purpose.