I've considered teaching law, but it's incredibly competitive and mostly reserved for those with better educational credentials than I have.. There are far less law schools than there are undergrad institutions.
I've run into the same issue. I'd love to teach law, and I think I'd be good at it, but my J.D. is not from an elite institution. I have a couple of friends who graduated from the same law school that I did, and they've been able to pick up adjunct/clinical classes. Full time, tenure track positions, however, are another story. Even at many T4s it's not unusual to find Harvard/Yale/Columbia grads with federal clerkship experience. I've met a few full time profs who went to places like UCLA, Texas, and Washington, but they all had some other unique experience that made them marketable.
The vast majority of law students would be better served by law schools' hiring great teachers rather than great academicians. It's yet another example of the obvious disconnect between the academy's notion of legal education as a purely intellectual pursuit, and the reality of forging a career in law, which most grads will be confronted with.