An underlying problem is that many of the HBCU's in Division I are not large enough and do not have the resources for athletic programs at that level. There's a history here.
These schools were founded in the days of segregated education (Mississippi Valley State University was founded as a segregated institution as late as 1950). In their glory days when most Black students and almost all Black athletes attended HBCU's there were resources for athletics, bands, and other activities--often state resources which, while less than what supported white schools, were nevertheless consistent (bribes, in effect, to keep Black students away from white state schools). The athletic programs of these schools were often highly successful--at one point there were more NFL player from the SWAC than from any other conference, and lots of white folks went to the games. The best Black students and athletes--and student/athletes--went to HBCU's.
Desegregation changed all that. Once it became clear that segregation in higher education was over, the formerly white schools recruited Black athletes and students and student/athletes, state fiscal support and, importantly, popular support of the local state segregated schools diminished (in Mississippi Jackson State and Alcorn may have been Black, but they had been "our" Black schools), and a lot of institutions found themselves--find themselves--with athletic programs at a level which they cannot support. Black students and athletes and student/athletes are much more widely dispersed, local and state support has diminished, but institutions resist downsizing from DI to DII or DII to DIII. No HBCU is going to win a national championship in a major sport; many could be highly competitive with schools their own size.
HBCU's are not the only schools to find themselves in this sort of predicament. But they are disproportionately represented in this group. They still have good students and good athletes and good student/athletes, but they don't have huge stadiums to fill with paying fans, or scads of assistant coaches, or squads of tutors. They're not overrepresented among the schools with athletes with academic problems because they're HBCU's but because they're smaller and overextended. Better all around if more of these schools were encouraged and enabled to "fight at their own weight."