This is a very interesting and constructive answer.
Diversity can be obtained by removing static behaviors in favor of dynamic behaviors.
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Done
Following this mantra, devs seems to have delivered the following mechanics so far:
Smartloot 3.0
60% specific, 40% generic, less legendaries
- Cons:
- Less item identity
- Pros:
- Rarifies good items and make them important
Decouple items from powers
Roll dynamic powers on legendary items
- Cons:
- Less item identity (Uniques to compensate)
- Pros:
- Any item can roll any power
- No more slot-lock
- 3D model decoupled from power
- Easier to add more 3D models
- Easier to add more powers
Remove sets
- Cons:
- Less item identity
- Less combo effect (more legendaries / slots to composate)
- Pros:
- No more 6-slots-lock
- More granularity and composability
- Player’s choice rather than developer’s choice
- Incremental power gain (don’t have to wait for the 6th piece)
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TODO
More RNG
Increasing the dynamic roll nature of items, as you suggest, is a great way to achieve more diversity (more chaos = more entropy = more surprise). 
For example:
- an item have a 10% chance to roll an affix that normally it should not roll
- an item have a 5% chance to roll an additional minor power
- …etc.
Unpredictability is key for a customized, tailored experience, which means more replayability.
More Slots
Increasing the number of gear slots achieves a parallel purpose which is extending the number of combinations.
This is a second layer of diversity. It does not impact the root layer of diversity which stays the RNG roll of items, but instead enables diversity of the build, by enlarging the size of your deck of cards.
With 51 slots:
Conclusion
Both directions are needed to skyrocket the build diversity. 