I appreciate your questions. I will honor them with the same dry humor by responding as if actually using ordinal dates were something many people did.
Leap years: A sidereal year adjustment may occur on any day, there is not a requirement for it to occur on a specific day. Leap years merely have an additional day identifier in the series before returning to 001.
Anniversary events: Again, there is no requirement that the memorialization of a person or event occur on a specific month and day. Many occurrences such as Mardi Gras and Eid using a lunar calendar or the USA's Thanksgiving using the day of week.
If one wishes to commemorate an annual event at the same orbital position as when it occurred, then ordinal dates are more effective since the Gregorian calendar's fourth-year 02/29 throws off any anniversary after the first 1/6th of the year.
NB: ISO 8601 "leap week" instances occur at a different rate than leap years (a more parallel construction would be "leap week" and "leap day"). "[The] 53 week years occur on all years that have Thursday as the 1st of January and on leap years that start on Wednesday the 1st."
https://en.wikipedia.org/wiki/Leap_year
https://en.wikipedia.org/wiki/ISO_week_date
A higher order number than ordinal and cardinal is ratio. We can also express the current day as how far through the year we are. Since today is 192, it represents 52% of a year, the ratio of current day to days in the current year. Below is an example in bash.
$ date '+%j'
192
$ echo "scale=2; $(date '+%j') / $(date '+%j' -d $(date '+%Y')'-12-31')" | bc
.52