Is there any reason as to why SEC schools don't have Division I wrestling teams?
I would guess it is all because of Title IX.
In order for SEC programs to field competitive, non-club, wrestling teams there would need to be another existing sports team eliminated.
I would have a feeling that if you went through and compared sport for sport the teams fielded by SEC programs and schools that have either a wrestling team (if there are any at the 1A level of NCAA) or a hockey team (like Boston College, North Dakota, etc.), you would find that those programs didn't compete in a discipline that the SEC does (possibly tennis or golf).