Public safety networks are different to commercial offerings ..
There are a lot of reasons why Public Safety networks do not use commercial GSM/3G/LTE networks most are technical, others are logistical.
Public safety networks are designed with extremely high availability requirements. The network I work on has site outages measured in seconds across the entire network and we have to account for each outage. All sites on this network have at least 8 hours battery backup and generators, I can't see many cellular operators going for that. Same goes for microwave backhaul systems which are duplicated and diverse. Cellular networks are not even close to the same reliability which costs a lot of money.
The type of traffic on a Public Safety network is completely different, its common to have over 500 subscribers on the same talkgroup (virtual channel) on a public safety system. PTT on cellular is a complete joke by comparison. Group calls outnumber individual calls by about 10 to 1 on the system I monitor.
Call setup times are different. Public safety networks generally guarantee call setup in less than 0.5 second. That fireman doesn't want to wait when he is in a burning building. Then you have dispatching centres which can join users and talkgroups on demand instantly whilst recording every word which was spoken on the network.
Then there are issues of encryption and authentication, cellular operators can do this but the costs are extremely high along with the consequent limitations on them changing their network without prior security reviews.
Public safety networks are designed to be used during civil emergency when power is off and cellular networks down. Cellular networks can sometimes be used as a backup if the public safety network is down not the other way around. Saudi Arabia
There are other reasons for not using commercial networks but I hope the list above gives an idea of some of the issues.
LTE is interesting as it is the first cellular technology which could meet public safety requirements with the appropriate applications (to be written) running on the handsets however the availability issues remain for commercial operators.