If You Have the Time...
I'm pretty sure Wait for the Mailman by the Mailbox Day was inspired by an episode of Leave It To Beaver.
I think you would only bother celebrating this day if 1) you have a mailbox, 2) you have a lot of time, and 3) you're expecting something relatively small and extremely important that you don't want anyone else to see and that you're certain is going to arrive via post today.
That doesn't fit a lot of people.
If most of the above fits you, you'd almost be better off hiring someone else to wait by your mailbox for you.
I will not be celebrating this day this year because I'm much too far away from my mailbox. I'm also not expecting anything that would fit inside it.
I am expecting some toys, but the sender told me via email that I'll have to sign for them (even though they're not that expensive), so I'll have to get them from the post office when I get home.
And that brings us to why this day is already largely outdated. Email.