>MyKC doesn't report on recommended tests
That is not the case.
Elbow scoring is not recommended in my breed or seen as an issue (out of hundreds of dogs tested in Scandinavia and USA all bar around 6 with a score of 1, have had perfect Elbow scores).
As one of my breeding who was grossly overweight at 6 months was given a tentative/suspected diagnosis of ED I had his litter sister Elbow Scored, and it is on her records and MYKC.
The only time eye tests won't show I believe is if there are no known hereditary conditions officially known in that breed and your testing just in case.
If your breed has a known condition and testing appears on registration documents then results will also appear on MYKC. Unfortunately in some breeds, among some breeders uptake of Health tests is poor.
For example in the USA the number one worst breed fr Hip Dysplasia statistically is the Bulldog, yet virtually none are Hip Scored here in the UK.