Great idea: When it is impossible to estimate a job/task/feature, just budget it. How much time is it worth? Can be build a minimum viable product in the time? This will allow you to develop the best solution in a given time. However, do not define the timeframe by estimating the size of the task…
Ah, the wonderful meaning of velocity. Velocity is often interpreted as a fixed development speed, and increasing the velocity means a higher development speed. What some people do not understand is that velocity and days (FTE etc.) and currencies with a floating exchange rate. When prompted to increase velocity, a team could simply estimate higher number for each story, increasing the velocity while keeping development speed constant or even lower.
Please refer to the article Increase My Velocity, Baby! for lovely unicorn images.
I came across a case study of how to estimate and slice stories in a real-world scenario. Everyone knows Adobe, and this is how they do it: Using Vertical Slicing and Estimation to make Business Decisions at Adobe.
The case study presents an actual problem which needs to be solved, and Adobe did not ignore it.