Last December AA denied me boarding on the first leg of an LAX CDG trip via JFK because I did not get to the checkin counter until 44 minutes and 50 seconds before departure time (yes, really). This violated the new, check your luggage 45 minutes before departure rule, evidently instituted rather recently.

My bag was too big to carry on, so, I got left at the counter. Ended up having to go to JFK, spend the night there, pay for a hotel, lose one night in Paris on a prepaid reservation.

So, checking bags can create its own problems.