Elaborations on mean_wQuantileLoss calculations: why is it weighted by abs_target_sum and why is it not calculated on a per-series basis in get_metrics_per_ts()?

[Serendipity31]

Because it is an approximation of CRPS, I'm interested in understanding more fully the choices that have been made regarding the calculation of mean_wQuantileLoss.

1. Why is each QuantileLoss[q] weighted by abs_target_sum? I have only found reference to the kind of weighting discussed in Gneiting and Ranjan (2011), but this doesn't make use of the target values in the way the calculation of wQuantileLoss[q] does.

2. Is there a conceptual or theoretical reason why mean_wQuantileLoss not calculated as a part of get_metrics_per_ts()? The information that is required to calculate wQuantileLoss[q] on a per-series basis appears to exist, yet this is not done. I'd like to know if there is a reason to refrain from calculating this metric.

3. Is CRPS supposed to be bounded [0, 1]? If so, how does the approximation of CRPS with mean_wQuantileLoss maintain those bounds?