Unfortunately, turbochargers are one of the first things people point to when there is a "low power" complaint. Because of this, there are many turbos that are misdiagnosed as defective, then removed/replaced that have nothing wrong with them.
On the other side of the argument are turbos that do have an actual defect or problem. If the technician doesn't take the time to determine the root cause, the replacement turbo will also have a shortened life on the engine.
In short, the turbo only knows what inputs it has. The operation is firstly controlled by the expanding hot exhaust gasses. If the EGT (Exhaust Gas Temperature) is too low for any of several reasons, then it would be impossible for the turbocharger to achieve the desired boost pressure: hence a "low power" complaint.
By adding complexity to the Forced Induction system, many other variables have been introduced. For example, a fixed vane turbo is only at its' maximum efficiency at one point on the speed/load curve. It is designed for peak torque/power at the rated speed of the engine, and anything above or below is a compromise. Conversely, a VGT turbo is theoretically at max efficiency anywhere along its' curve…unless something goes wrong. A typical problem with a VGT turbo it that the sliding vane system gives the turbo the ability to "adjust" to the differing boost requirements in the exhaust air stream. This means that any excessive amount of carbon, a wet exhaust from a leaky injector, or any of several similar problems will cause the vanes to get stuck, rendering the turbo to be at max efficiency at only one speed, and horribly inefficient at any other speed (think lots of black smoke and very low boost/power). If the problem isn't fixed, the electronic actuator will fail, either electronically or the physically (gears will strip or shaft break).
Turbos have been designed to last the life of the engine. Any failure needs to be researched to determine the actual cause of failure. Turbochargers have also gone through many design changes brought on by the increasingly stringent emission requirements, and the quest to come up with new methods (and equipment) to meet those goals. This has taken a very simple design of a "fixed vane" turbo and introduced VGT (Variable Geometry Turbo) that have many more moving parts and issues than their predecessors. There are also dual compound turbo set ups, dual scroll turbos, and there will continue to be more design evolutions as demands and technologies emerge.
A good technician will investigate to see what outside influence has been the primary causation to the failure of the turbo. With the introduction of the EGR system, the VGT system, issues with a wet exhaust, oil contamination, electronic controls and circuit failures and air leaks/dirt ingress, there are many contributing factors to consider.