HBC's have a branding problem. Even black people don't want to go there.
Most of these colleges need to rebrand and completely shed any association to being a historically black college. They won't do it because of optics and are stuck being considered sub par universities.
Why would anyone white go there? Very few do and that's reality.
HBC and small liberal arts colleges are suffering the same fate of low enrollment. Many of these universities need to make deep cuts or close. However, that goes counter to the narrative that these colleges are both needed and doing well.
As an HBCU alumnus of Florida Agricultural and Mechanical University (FAMU), allow me to give some insight.
White people go to HBCUs because of the economics. White students average about 10% of all HBCUs' student bodies. I recall a story of a guy who went to Tallahassee Community College (TCC) and wanted to transfer to Florida State University (FSU) to major in mechanical engineering. He got turned away. Since FSU and FAMU share the same engineering school, he applied to FAMU and got accepted. He attended the FAMU-FSU College of Engineering and got his Mechanical Engineering degree (the same place where I got mine).
Plus in the midwest, a handful of HBCUs have majority white student bodies like West Virginia State University and Bluefield State University and Lincoln University (the alma mater of a family friend in Kansas City graduated). In the case of Lincoln, a lot of state government workers in Jefferson City, MO send their kids to Lincoln because it's way cheaper than Mizzou (University of Missouri).
At FAMU when I was there, most of the architecture majors on campus were white. And since FAMU had an Army ROTC and FSU has a Navy ROTC, many white FSU students who wanted to be army officers came to the highest of 7 hills in Tallahassee. Full disclosure: There's a drug deal of sorts in the FL capital where, if one university has a college that the other doesn't, the students from both universities have to share it. The taxpayers don't like coughing up green to give colleges to two universities that are just 5 miles apart.
The public HBCUs (such as FAMU) tend to fare better than the private ones, in part due to sheer size. But, FAMU has around 10,000 students, nearly 2-4 times larger than private HBCUs. I believe North Carolina A&T is the largest with 14,000 or so students.
If white parents can send their kids to an HBCU to get a degree without selling their vital organs or grandchildren in the process, they'll do it.