If it makes you feel better.... On February 29, 2008 I was working on a system as a government contractor. Part of it was outsourced to a sub-contractor who decided to write their own date/time library because how hard could that be (which I only learned about later)? For some reason NOTHING would work right that day. Took me longer than I'd care to admit of staring at the logs to realize that some started with March 1 2008....
Definitely not any more coherent on a leap year! That remark only applied to dates stored without a year, as in “February 29” rather than “February 29, 2008”.
Whenever February 29 wasn’t present as an option, the frontend was at fault, so I could set the right <input> value in the inspector as a workaround.
Other times February 29 was present as an option, only to be saved as February 28. Never March 1, which I’d say would be more coherent.