Your cliff jumping metaphor is a great one and it makes the answer obvious to me.  "Why do we keep implementing change like this?" Because it's more fun and there are relatively few consequences.  Okay I am being a glib. However, having spent 20+ years in strategy execution as an internal and external in a couple of dozen organizations, I have come to believe that there are systemic issues - as in ‘built into the systems and culture of the organization’.

In back rooms people will tell you: "this is the third time we are taking a run at this strategy", "people may get fired but that's rare" or "those who get fired are charged with executing the strategy not those who designed it".  There is little connection between what is the ideal strategy for the organization and what is the feasible strategy for the organization.  Those in execution are always preparing the contingency decoys (they have to because it is a survival technique), i.e. the initiative fell short because ... x competitor changed their strategy; y change in external environment (economic collapse, FX rate blind side, etc) or z supplier failed (delivered late, over budget or inferior product).

The real problems are more like: executives are more focused on quarterly reporting than they are on 3 yr strategic plans (compromises always undermine the long term); this is too much change for the organization (i.e. bandwidth, adaptation capacity); the independences (read cross-silo) are not well understood; leaders are not fully committed because they have to hedge for survival, promotion, next move.

I would add to the excellent points above:
- Stop jumping into strategy. I know, feels like plenty of time is spent upfront?yet, still we fail.  Invest more time in better planning. Try a few different things: play through the strategy with the whole team and probe the cross functional implications; bring those executing into the strategy process and make those designing strategy work in the business, on the floor.  “In theory, theory and practice are the same. In practice, they are not.”Albert Einstein
- Jettison the notion of ‘creative tension’, i.e. when executives have to compete (for ideas, resources, power, etc) they perform better. This is a fallacy. The only way to succeed going forward is to collaborate.  Internal competition is toxic to collaboration. Collaboration is a major culture change?invest in it appropriately.
- Stop firing people for failing - fire for incompetence. They are actually qualitatively different tho hard to differentiate.  You want to keep competent people who failed so that the organization does not make the same mistake next time.
The obvious answer is this: if we want different results we have to do different things.  Alas what may be obvious is not simple.

Great post-really fired up my brain today.  I will be further developing it for my blog and will reference back here as well.