HB730 would have made that happen:
Four candidates shall be appointed upon the recommendation of the President Pro Tempore of the Senate. Four candidates shall be appointed upon the recommendation of the Speaker of the House of Representatives. One candidate shall be appointed upon recommendation of the Minority Leader of the House of Representatives. One candidate shall be appointed upon recommendation of the Minority Leader of the Senate. Two members shall be appointed by the Governor.
That would still leave Berger & Moore appointing 2/3 of the UNC Board of Governors (8) vs the Democrats 1/3 (4). But this bill was immediately buried in committee and did not survive the Crossover. Because in the minds of Republicans, the only thing more important than power is absolute power. This bill would also have slightly modified appointments to (each) Board of Trustees:
Except as provided in G.S.116-65, each of the 16 institutions of higher education set out in G.S.116-2(4) shall have board of trustees composed of 13 persons chosen as follows:
Eightelected by the Board of Governors. Four members appointed by the General Assembly under G.S.120-121, two of whom shall be appointed upon the recommendation of the President Pro Tempore of the Senate and two of whom shall be appointed upon the recommendation of the Speaker of the House of Representatives. Two appointed by the Governor. The president of the student government ex officio.
When Republicans took over the General Assembly back in 2011, one of their first major power grabs was creating a 4th "Branch" of government. Each Legislative house was granted the same privileges as the single Executive. So instead of appointments being 6 vs 6, they became 4 + 4 vs 4. But now? Even that painfully unbalanced formula is not acceptable.
The system needs to completely change
The way I would do it is to require that all of the UNC BOG members have to be confirmed by the faculty senates of the individual universities in the UNC system.
The problem we have here is that there are political appointments being given out as a "perk" to influential donors or to push a particular ideology. If a candidate proposed isn't confirmed by faculty, another has to be nominated.
The universities themselves are the ones most impacted by these decisions and the faculty who make the teaching and research work should have the final say on the leadership.
If Democrats ran with this as a platform, they might spur more turnout from faculty, staff, and students in the UNC system simply because the Republicans have destroyed all sense of trust in the UNC system leadership.