Their stars are underperforming
These issues are not ranked in any particular order, because honestly, you can make an argument for almost any of them to be their "biggest issue". And a lot of them affect or are affected by the other problems that have arisen. But at the end of the day, teams will go only as far as their stars will carry them, and the Cardinals' stars have not done that this season.
Coming into 2023, the Cardinals were banking on Paul Goldschmidt and Nolan Arenado, the reigning National League Most Valuable Player and the third-place finisher, and newly signed Willson Contreras to be their three "stars" in their lineup. As I and many others said, the lineup depth they had built meant they could have even more borderline, or in the case of Nolan Gorman, legit All-Star bats pop up, but they needed their top three to lead the way.
Here is how the Cardinals' top three bats have played so far this year.
Paul Goldschmidt: .288/.382/.488, 11 HR, 31 RBI, 141 wRC+, 2.2 fWAR
Nolan Arenado: .283/.331/.488,13 HR, 45 RBI, 122 wRC+, 1.4 fWAR
Willson Contreras: .198/.292/.347, 7 HR, 27 RBI, 81 wRC+, 0.2 fWAR
Each of them has seen significant regression in their wRC+ this season. Goldschmidt was at 177 wRC+ last year, Arenado was at 151 wRC+, and Contreras posted a 132 wRC+ for the Cubs. These aren't just the slight regressions that you'd expect for each of those guys after having career years, they are big drop-offs from the players they were.
In the case of Goldschmidt and Arenado, they both have had stretches where they look like their 2022 selves again, but they've also both gone through multiple ice-cold streaks that have really hurt the offense. For Contreras, he's been in a funk the majority of the season, and the fiasco with the catching situation surely hasn't helped him feel comfortable in St. Louis.
Would the Cardinals be in a great position if these guys were playing to their standard? No. But I really do believe they are not in as dire of a situation as they are now.