IMHO would be a bad idea.
Because, it is much better to cancel a card when or before the end of the annual fee waiver for a new account ends rather than trying to keep it open by "downgrading" to a new, fee free, card. If you cancel you can get a new bonus at some point. And, bonuses are what let us fly in F.
Plus, it's called a downgrade for a reason. The miles earned are usually half those on the original card per dollar spend.
Cancel card when fee comes due or before and move on to a new card.