As someone who has worked in DT Jxn for 30+ years (and still does), DT is not dangerous at all. There's little crime, although homeless do pass though as Gateway Mission is nearby.
DT is deserted though, it was vibrant in the mid 90s with folks everywhere, now it's largely abandoned. There's no bringing back the professional firms, as they have invested in infrastructure in Flowood, Madison Ridgeland. Just drive Highland Colony Parkway and you see several buildings of firms that once populated DT.
Building the ballpark DT wouldn't have made difference, it would have been mismanaged and sit empty most of the time, much like the Convention Center.
I'd like to see an entertainment district DT, Beale Street on a much small scale (I know that failed on Farish St). City/State leaders would have to be willing to invest in over the top security though, and I doubt that would happen. I was recently in Austin, the police presence downtown near the bars, restaurants and clubs was impressive.