Here's why:
* Different bellhousing: The 6L80E from the 2500HD has a different bellhousing pattern than the 4L60E used in your 1500. The engine and transmission won't physically mate.
* Torque capacity: The 6L80E is designed for significantly higher torque than the 4L60E. While it *might* handle the 5.3L's output, other components in your 1500's drivetrain (driveshaft, differential, etc.) are not built for the heavier-duty 6L80E. Using it could lead to premature failure of those parts.
* Computer compatibility: The transmission control module (TCM) in your 1500 is not programmed to work with a 6L80E. This would require significant modifications, potentially involving custom programming, which is complex and expensive.
* Wiring harness: The wiring harnesses for the two transmissions are different.
In short, while there might be *some* very advanced and costly ways to make it work, it's simply not practical or recommended to try to put a 6L80E from a 2500HD into your 2001 1500. Sticking with a replacement 4L60E is far more sensible, cost-effective, and reliable.