In the end, why put hours on the bill if you don't actually wanna charge per hour?

You do charge per hour, except the "hour" is an abstract measurement of the cost (in terms of labor) of some task. That number is also an estimate because you don't know ahead of time the specific factors that will affect the actual labor it takes to do that task.

So it serves to purposes:

1) provides a standardized unit to measure labor for the purposes of billing. how do you determine what the labor cost of an oil change vs a gasket replacement vs valve timing adjustment? Hours is the unit used here

2) provides a target to negotiate a work contract. the shop agrees to do a task, and estimates that it will cost N hours. The customer agrees to this and the work is done. If it takes more than N hours the shop basically eats the cost.

In the end, your opaque "$N for X task" system effectively includes a hidden "N hours @ $Y/hour" cost anyways. The only thing you're arguing for is making that opaque to the customer.