For the most part, I would agree with you. However, the point could be argued that since locations are allowed to prohibit carry, the point could also be made that locations could also impose additional requirements for carrying on those properties, or restrict carry only to "authorized" persons. I for one would propose a voluntary program, which I have discussed elsewhere. (I would describe it here, but since I received a strongly worded PM regarding posting my sentiments in multiple places, I suppose I'll just leave it at that.
Locations being "allowed" to permit citizens to carry or not to carry a firearm is not codified in all states and therefore it is not a violation of law to carry. Trespassing a citizen who refuses to leave then becomes a violation of law not technically associated with the firearm. You could be trespassed at a school for wearing a shirt with "offensive" text or images. Additional requirements placed upon "employees" is a condition of employment and not, that I am aware of, required under any states statute until additional requirements are codified into law.
Well remember though, we're not just talking statute, we're also talking civil and contract.
if a school authorizes a teacher to carry on premises, and that teacher kills someone over grades, is that a civil tort against the school for allowing it?
lets not even talk about what L&I will think about paid employees carrying guns on the clock all the time, probably already some structure for administrative rules regulating that. much as you'd like to think otherwise, allowing teacher carry like you propose would require a significant change in terms of regulations, laws, legal culture etc that has built itself up over a century. not easy to do.
Interesting perspective. What mechanism holds Sandy Hook harmless from being sued in a civil tort for wrongful death? CT is a shall issue state as far as I know, however that is tangential to this discussion. Unless CT has laws that specifically prohibit the carry of a firearm by a citizen, any citizen, on school property as the GFSZ Act does allow, via a "state license", then the argument could be made in a civil court for wrongful death. This in turn could hold Sandy Hook and the school district accountable for not permitting the adults to be armed for self defense as CT law allows, if CT law allows. Missouri does technically allow carry on school property. The reality of a citizen carrying on school property is a different discussion.
A change in laws may not be required, just a change in the district and school policy (employee) handbook. The difference between a "state school" and a private school (business) is that the state is prohibited from infringing upon a citizen's RKBA where a private business (citizen) is not so encumbered.
If any of those poor souls who lost a child are a 2A supporter, I would recommend that they sue that school, the district, and every administrator for the wrongful death of their kid(s). Let the courts (the state) tell parents, once and for all, that the state mandates that parents are not permitted to protect their kid's right to happiness, liberty, and more importantly, life. Remember, the state currently mandates that a child has no right to protect themselves via the 2A. The state mandates that any adults present are not permitted to protect kids in any school (that Texas school and the few others notwithstanding).