As someone who had this job (although in a local, not a national), and who also could be fairly described as “quiet, reserved, and introverted,” here’s my take on it. First, fraternity president is not a good job, it is thankless, stressful, and can be challenging. Second, the fraternity president is not really the leader of the house, in the sense of the natural hierarchy young men tend to form in that environment. The most important part of the job is really administration-facing and as a point of contact for issues that arise with other houses; it’s part White House Press Secretary, part complaint line, part admin bs. (Animal House captures the spiritual truth of this role to some extent.). That said, there is no question that if this is his role, it’s a sign that he’s respected and trusted by the guys, recognized as responsible and someone people can bring problems to. If this were my son, I’d be proud, that kind of respect from his peers means something.
The liability concerns are real but manageable. My suspicion is that the large national organizations have relatively robust safeguards against excesses in the pledging process these days; back in my era, in a local fraternity, it was much more of the Wild West and I had a great deal of anxiety that someone was going to go rogue and do something stupid and dangerous, but blessedly that never happened. But being the president means the challenges fall to you, and I had a number of crazy experiences, mediating disputes between drunken brothers to de-escalate violence, dealing with unwelcome guests at the house, dealing with a few challenging disciplinary situations. I might make sure i had a good umbrella policy that covered him, if possible and just in case, but that’s probably excessively fussy risk management.
Bottom line, while it’s a thankless and crappy job, for me it was a very valuable learning experience and one I look back on fondly. He’ll be fine; it’s not the 70s or 80s anymore, almost certainly nothing crazy is going to happen.