Why does the Clinical Journal of Sports Medicine think they will need quadrillions of DOIs?
This "answer" is really speculation - if you truly want to know their motivations, you have to ask them.

But I think the simplest and most likely explanation is that they don't consciously believe they will need that many DOIs; they just had to pick some format, and arbitrarily chose a number of digits that seemed more than adequate (as well as perhaps allowing for DOIs to be assigned in some other way than just serially; e.g. someday the DOI could identify volume, year, page number, etc).  

They probably didn't even think about people needing to transcribe them by hand - and to be fair, in this age of electronic distribution and copy/paste, it's a pretty rare use case.