For quite some years every other Sunday I'd leave home1 early evening and arrive at home2 early Tuesday morning, having travelled on average about 21 hours (all those mandatory inspections of my underpants, you see), thereby skipping an awful lot of Mondays.
A day really is just a thing: I'm not any younger.
While you're right that crossing the IDL doesn't make you a day older or younger... there is a slight flaw in your logic. In order for you to have gone forward a day every two weeks, you must have come back a day in between, as well.
After all, it's possible to fly around the world in less than 24 hours, but you can't use that to travel forward or backwards in time, you can only ever get to a maximum of 24 hours ahead or behind of another place.
Perhaps I was too dry: everything you say is true, but you kinda missed the point ;)
Edit:
In retrospect realise that wasn't particularly helpful. I skipped an awful lot of Mondays for which the only consequence was utter joy at the two cocktail hours every other Saturday. Contrary to the great grandparent, a day really is just a thing.
Sorry, I wasn't clear enough - I didn't miss the point you were making, and I completely agree with it (one of my other comments somewhere on this page makes that same point), I was just pointing out the flaw in your example that travelling forward through time zones many times won't make more of a difference than doing it just once.
A day really is just a thing: I'm not any younger.