Why use percent and average for improvement projects?

It seems that every healthcare quality improvement presentation I hear nowadays uses averages and percents as the mechanism for demonstrating an improvement was made. I have some problems with this:

1. There seems to be a confusion between performance management and measurement for improvement. Yes, the organisation may need to report on the % of x - done mostly so someone in charge can make a comparison. However, this is no reason to replicate this measurement in the project. For instance, if you're working on length of stay (LOS) then you may find mode (most frequently occurring number) is more helpful in demonstrating a change consequent to your improvement activities and it has the benefit of indicating the experience for most patients.
2. When a nurse pointed out to be that they do not have .32 of a bed then I took notice. Of course she was right. So some stats that showed an average of 12.32 beds were to be shifted each month (a specific project) I could see this was nonsense. Statistically it could be argued this made sense, though as a mechanism for engaging staff, working in whole numbers, whole beds, whole patients, tends to make more sense.
3. So ward A delivers a 4.18 average length of stay. Management now want all wards to achieve this (let's assume most are higher than this). So the processes and procedures underway in A is replicated to others (or attempted). The difficulty is their case mix may be different, their problem may be one where only their long stayer need to be addressed (they have the same mode but ave stats skewed the total figures) etc. In aiming for an average do they figure out the mathematics of LOS - x number can be 4 days, y number can be 5 days etc? For this is what the average leads them to - to game.
4. An average, is, by definition, an abstract concept that assumes half the values will be above the line and half below the line. Do you really want to have half your experiences, interventions etc be more than the agreed number?
5. One more measurement challenge. What happened to the 100% (or 0%) target? The common version is 98% of y or 95% of z. My logic suggests we are designing systems for a percentage failure. This is a tough call in healthcare. Which 2% of patients will you choose not to have optimal care for their diabetes?