Dollar is getting stronger and stronger only against other fiat currencies but it is not getting stronger actually. Because around 100 years ago we used to buy much more things from $1 than what we can buy today. This clearly shows how negative dollar's value has gone and this will go even more down as fiat are meant to be in such a way.
I think it's because the USA is a powerful country all over the world the reason why the value of its fiat is big and dominant compared to another fiat. Well, Since Europe it the motherland of the USA so maybe there is a possibility if they will allow it but I think this time it's too hard to predict since the dollar has different features compared to the euro.