Congratulations on finding a very fine KitchenAid KDS-37, which dates to between 1971 and 1974. The "S" stands for Superba, or top of the line.
I just bought a KitchenAid KDC-37, Stainless Steel Sink/Dishwasher combination unit, virtually the exact same as your unit. The "C" stands for Custom, and was the bottom of the line. I picked it up in Buffalo, NY last Saturday November 20th, and brought it home. Yesterday, Todd (varicyclevoice) and I were just studying my machine to answer the exact same question you are asking.
The dishwasher is secured to the cabinet with screws from the back, front, and through the side from underneath the sink. So if doing this properly, one would need to disconnect the unit from the water supply, drain and electrical service. Then pull the unit out of it's current position.
I have seen firsthand on several occasions, this kind of separation having been performed on other Sink/Dishwasher combination machines (these machines are usually called Electric Sinks). The most common separation being performed on the GE units from the 1950's. Those dishwashers were never meant to be removed, so the cabinets were cut with a hacksaw to remove the dishwasher.
Fortunately, this separation process is much more practical, and less painful on the KitchenAid Electric Sinks, but nevertheless, it still is / will be a time consuming project, if you wish the cabinet and stainless steel drainboard to remain in good condition. Once the old dishwasher is removed, a new/modern dishwasher should just slide in underneath the stainless steel drainboard, and reconnected to water and drain.
You asked if the dishwasher has any value. Personally, to me, the dishwasher itself, having been removed, would be much less of interest to me. I say this mainly because the model/serial number plate inside the door of the dishwasher, on the left, will read KDS-37, meaning it was originally part of an Electric Sink. Since I collect Electric Sinks, I would much rather have the entire unit. The KDS-37 unit is an Electric Sink, which happens to have a stand-alone KDS-17 dishwasher installed inside the outer cabinet. Those stand-alone dishwashers can still be found, and not at all yet considered rare. Therefore, in my opinion, the KDS-37 dishwasher itself may not be that desirable, EXCEPT, however, for parts.
In closing, these dishwashers from this era were very good machines. And I certainly would encourage you to get to know it some more, and continue to use it for a while longer before making the decision to swap it out for something more modern.
Hopefully, we will get some additional opinions from other members regarding how you might want to proceed.
Good luck. Mike
