The park has many weaknesses.
#1: Its competitors (such as Holiday World and Kings Island) have more room to expand, while Kentucky Kingdom's size if it uses all the land for expansion, would be around 80 acres, far smaller than those two other parks.
#2: Height restrictions, given its proximity to the airport, restrict KK from ever building attractions taller than 150 feet (which, as far as I'm aware, is the max height they're allowed to build), which limits the park if they ever plan/want to compete by building new thrill rides as they did during the 1990s.
#3: (This is a minor one, but no one I've seen really talks about it as a negative) The park layout is terrible. The road cutting the park in half, King Louies Playland being in the middle of the front half of the park, and Hurricane Bay being in the middle of the second half of the park make KK unnecessarily difficult to navigate (especially when compared to Kings Island, for example). The back half specifically feels dead in most places, such as the area between Thunder Run and Taco Tequila, which is connected by a long, narrow path, with only one attraction (Raging River Rapids Ride) and almost nothing going on back there.
#4: KK, despite its best efforts, has so far struggled to make a profit. When Hart reopened the park in 2014, he believed that KK in the 2010s could have 1.2 million visitors in a season, which were the same attendance numbers from the '97 season. These days, Kentucky Kingdom gets around 700k visitors per season, which is not terrible, but far less than its competitors who average over 1 million guests per year. The issues with making a profit limited the park in the 2010s when it came to new additions (such as not being able to afford a dueling RMC, instead opting for a single-track Storm Chaser). The emergence of Holiday World may be a reason to blame their attendance struggles, as I know that park has taken a large bite out of out-of-state visitors who now go to Santa Claus and not Louisville,
I should mention the park of course also has its strengths, its location in Louisville and friendly relations with the local and state governments definitely help it. But barring some serious investment from Herschend or some other operator, I don't understand how Kentucky Kingdom can stay open without heavily relying on the state and local governments to help bear the cost of keeping the place afloat. Although I wouldn't entirely blame Herschend's few investments for the current state of the park, because aside from the 1990s when Paramount was not expanding Kings Island as much and Holiday World was not much of a competitor, it seems that Kentucky Kingdom has struggled to really compete as a regional amusement park.