This isn't as big of a problem as many people first assume, but it's one you need to watch out for if it applies to your specific training needs. Most instructors would agree that a generic simulator is for most ab-initio training activities equally as good as a highly specific one. There are cases where highly accurate type specific simulators are required which is why operators spend tens of millions of dollars on highly sophisticated Level D Full Flight Simulators. For airlines Level Ds are a must. A Level D FFS allows a pilot to count all simulator time the same as in the actual aircraft; one to one. Not taking a revenue producing asset off of the flight line saves the airline a lot of money and the Level D gets the training done.
If you have a very specific training which you think requires a type specific simulator you will need to evaluate the importance of that need in relation to the cost of having such a simulator. Simply wanting more accurate representation of your aircraft can usually be satisfied with what is regulatory speaking a generic simulator, built to high fidelity. However if you need to do zero air time type ratings you'll need a simulator which can be used for that. It's important for everyone buying a simulator, to evaluate just what they intend to do with it, and what will be required. That evaluation is referred to as a training requirements analysis (TRA).
Most simulators are not Level C/D but can be type specific. Higher level type specific FTDs will have the aircraft cockpit and systems replicated exactly, but not be motion based. These systems are significantly lower in cost, can be implemented into training programs and be allotted credited time in terms of hours and tasks. For ab-initio training generic simulators are generally ok and they represent a class or family of aircraft in a more generic way. This is perfectly suitable because these simulators are generally used to train procedures for a specific license or rating, not specific aircraft. For example, in an ab-initio flight school a student needs to learn about how to read an altimeter, the difference between the altimeters in any two similar aircraft is a relatively minor point.
While not an FAA requirement most insurance companies, for complex aircraft, will only allow AATDs and FTDs to be used to qualify for insurance purposes that are aircraft specific.
If you're an operator who only flies one airplane or helicopter, or multiple identical aircraft you may wish to consider the high fidelity route because it's going to give you a closer fidelity of simulation to your actual aircraft.
If you want to provide more general training, or operate multiple similar but not identical aircraft you will likely want to have a more generic flight simulator which replicates a class of aircraft; for example single piston engine light helicopters.. That way your simulator can be built more generically and you do not have to worry about exactly replicating a particular aircraft in the smallest detail. Its purpose is mainly to teach procedures and in some cases specific (hovering for example) skillsets.
The reason this saves money is because accuracy is surprisingly difficult as aircraft vary widely. Therefore there is much more work to be done, both in terms of software, and hardware. Most simulator manufacturers have a large library of general flight models[^a] for various types aircraft on hand. For example we have many different aero models[^b] which allow us to build sims which generically represent almost any aircraft both fixed and rotary wing with reasonable, but we may not have one to meet the exact precision requirements for a type specific simulator for your specific aircraft. Generic modeling goes to trend and magnitude of flight characteristics. For those aircraft we generally do a bit of flight test and then modify the aeromodel appropriately.
If you came to us with a requirement to build a flight simulator which exactly represented your specific aircraft, and to get it certified at the highest levels of FTDs, we would have to conduct a more extensive flight test data collection effort. That generally results in added cost. Aircraft manufactures must use certified components such as switches, lights, and breakers which are approved for aviation use. Those components cost significantly more than their generic commercial counterparts. Because of the way simulators are built it's often not cost effective to use the aircraft components. Less expensive commercial equivalents can be use in the simulator and look, feel and operate identically to the aircraft. If we have to use real aircraft parts, that also adds to the cost.