Another major problem with the "all-in-one" metrics is the desire to apply them over any time scale and have consistent results that will sum.
The nature of hockey statistics is that no statistic perfectly describes the exact contribution of a given player to the result that was measured. The best we can do is look at our population of outcomes, determine which statistics describe the contribution of the player toward winning, and assign a corresponding value to those statistics. The resulting metric will be an estimate, not an exact measurement.
Since those values are derived based on the population, they may need to be regressed when applying them to a smaller sample. But the amount of regression that is needed depends on the size of the sample. No all-in-one metrics in hockey will change the amount of regression depending on the size of the sample, because they want the metric to be consistent in terms of game totals adding to seasonal totals adding to career totals.
Let's say an all-in-one hockey metric is created that uses the principle that observed shooting percentage is part randomness and part skill. So player shooting percentage is regressed partially towards league average in order to remove the randomness component, and the amount of regression is picked with reference to the amount of randomness in single season shooting percentage. The problem is that this will overrate the skill component and underrate the randomness component in single game shooting percentage, and it will underrate the skill component and underrate the randomness component in career shooting percentage. When a fixed regression figure is involved in a metric, the metric is only accurate for a particular sample size. In this case the metric would be a valid estimate for single season value (assuming we knew nothing else about the player but his statistics for that season), but not for single game value or career value.
This is an unsolved problem in WAR for baseball. There is not enough regression involved in their fielding metrics over a partial season, which means too much value is given to defensive statistics over a partial season. Similarly, there is too much regression involved in their fielding metrics over a career, which means there is not enough value given to defensive statistics over a career.
The entire problem is based on a misunderstanding of the all-in-one metrics. They are estimates, not counting stats. One possible solution is regressing single season numbers and/or single game numbers to a player mean based on the player's performance in other seasons instead of a general population mean. But I haven't seen any interest in that among the creators of all-in-one metrics - probably because it makes the calculations much more time-consuming.