Won't privatization save money and make services more efficient?

No. It is shown repeatedly that privatization (cutting an essential service and have it taken over by private sector business) raises costs and makes a less efficient and more confusing service. Services that get privatized and put in the hands of various competing businesses almost always wind up providing inferior services that duplicate and compete with each other, and they charge the consumer more for them. 

Privatization most often results in inequality of access. Whereas a public service used to give everyone access, or try to, regardless of profit, a privatized service must make a profit. If the STC is "successfully" replaced with private businesses, we will see only the STC's most profitable routes served. When a service is run by government, it doesn't matter if routes lose money.

If it's no good, why do so many governments advocate that privatization is a better solution?

Privatization is often a political scheme to transfers our collective wealth into private hands, depriving our government of needed revenue to balance a budget. It's often proposed by governments backed by the business lobby, because businesses actually stand to profit from the loss of a service that was previously available to everyone before privatization.

Frequently, before they privatize a service, government often abandons efforts to run the service well. By doing they ensure that not many people will care about it when it's gone.

With what it calls the "wind down" of the STC, the Saskatchewan government is embarking on an even worse privatization. It's not even selling the STC, it's abolishing it and letting businesses start completely from scratch.