"But the Intel shortage has nothing to do with 10 nm. That is a lie Intel is promulgating."
- in 2018, Intel had 4 active 14nm fabs and 2 unused 10nm fabs
- in 2019, Intel has 5 (a 6th fab is coming online or may already be producing) active 14nm fabs and 2 (3 in 2020) underutilised 10nm fabs
As you mention, core counts are increasing resulting in a decrease in die's per wafer (~33% less production capacity) and in some cases Intel is doubling up existing die's in the finished product (i.e. effectively a loss of 50% production capacity).
If you put arbitrary numbers per fab, once Intel have all 6 14nm fabs up and running they will only match their capacity at the beginning of 2018 before the latest core count war started.
Having 2+ idle 10nms fabs is the primary issue as it results in a 33% capacity decrease. While I acknowledge not having newer designs (i.e. more IO/memory bandwidth) to allow them to compete with AMD or a chiplet type design for larger dies doesn't help either, they are single figure percentages.