Valid point, but there are key legal and practical differences. I am not a lawyer and I may not be read up on all the recent cases, but I am a police officer and I have looked into this area a bit a while back.
For example, police officers acting in their official capacity (regardless of who pays) are generally entitled to qualified immunity. While private guards may qualify for qualified immunity in some circumstances, the law there is much less clear and their use in actual roles requiring action (rather than just observing and reporting) can be a major source of liability.
That is, Facebook would generally be liable for actions taken by private security working directly for them. They set the policy the security guard follows and are liable for the consequences of that policy. Police officers, on the other hand, work for the city (or county or state or federal) and their actions are generally governed by policy and law, which may act as a buffer between Facebook's deep pockets and potential lawsuits.
Additionally, even in states where a citizen's arrest is perfectly legal, there are logistical concerns. In the states I am familiar with, resisting an officer who is effecting a legal arrest is illegal and in some states even resisting an illegal arrest is illegal unless certain other elements (i.e. risk of physical harm) are involved. When a citizen is attempting to effect the arrest, it is much easier for the person being arrested to simply claim they were being assaulted and fought back and there is no simple way to determine who is right.
Having a trained, experienced, uniformed police officer effecting the arrest undercuts this argument because it isn't (generally) reasonable for an individual to claim they were being randomly assaulted by an on-duty officer.