The word "by" can be omitted. It doesn't change the meaning. I think it's there for rhythm. The spoken sentence would emphasize the "plunged" and "23%", and having an unemphasized word in between makes it sound better. You could say, "The number of shoppers plunged 23%," but it just sounds better to say, "plunged by 23%." When the "up to" is added, then those words are unemphasized, and you don't need the "by". It's more standard to end the sentence either "since then" or "from then on". "Since then on" isn't typical.