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Besides that, the lens used in a compact camera would not cover the full size of the DSLR sensor. The lenses are so small because they only have to "spread the light" enough to cover a sensor that is either 5 or 7 mm wide. A DSLR sensor is from about 22 to 36 mm wide. You'd end up with a circular image in the center of the larger sensor.

Assuming you could even pull this off. Theoretically.

Since you'd just be moving the sensor from one camera to another, you'd be getting the same images. Though, there would be a pinhole of an image due to the small lenses of compact cameras.

It's like putting a huge engine into a car too small for it. You'd have awesome power, but no way to harness it.

Besides, you'd soon be frustrated by the lack of flexibility in the non-interchangeable lens body.

You are thinking correctly.