The airport isn't a great example here. There are 3 lines because there are 2 different parties involved: the TSA, which has authority over the security checkpoint, and the airport/airlines, which have authority over the lines leading up to the checkpoint.

The regular line is self explanatory. Precheck is solely run by the TSA, and they politely ask the airports to set up dedicated lines for precheck. Sometimes they do, sometimes they don't. Until passengers are in the checkpoint though (i.e. beyond the id check), the TSA has fairly limited authority. The airport is ultimately responsible for getting passengers to the security checkpoint, subject to some minor conditions by the TSA. Clear pays the airport/airlines a kickback from the subscriptions to let their agents manage the queues, which includes putting their subscribers in front of the other lines. One thing they can't do is give you special perks inside the checkpoint like precheck does.

So, 3 lines because 2 different parties get revenue from one each.