We have sailed 11 times and at-port upgrades were available twice, and both times were very unusual situations (the first one was when there was the
disney+ "kids sail free" promo that included every room category EXCEPT concierge, and so many families booked that the kids clubs reached capacity and
DCL had to show the cruise as sold out to families with kids club age children, even though concierge still had rooms available. The second time was a day after the airport and port opened after a major hurricane and sadly a lot of people couldn't get to the port and missed the cruise).
For the most part, Concierge tends to fill up--yes it is expensive, but there are a lot of people celebrating special occasions (e.g., a milestone birthday or anniversary) or getting married/honeymooning on disney cruises, grandparents treating the family, as well as just guests who just have a lot of money. And not a lot of concierge rooms, because the whole point is that it is somewhat exclusive and provides a quiet retreat away from crowds with extra personalized service.
The best way to increase your chances of getting a discounted upgrade at port is to book a cruise close to the sailing date when you see there are still a lot of concierge rooms available. Other than that, if you want concierge and it is in the budget, you should probably just book it, since odds are not very good of getting it at the port.