The problem I have with this is that verbal description is an imperfect method of conveying this information.
It's an imperfect world. Just like IRL we cant ever know the probabilities of success for any given task, neither should the players.
I recall a thread recently where a poster stated his LG (or N - I cant remember) PC tossed a warhammer at a fleeing child thief 'aiming for his legs to knock him to the ground'.
He performed the action because the DC was set for the task by the DM, and he was aware that the consequences did not involve a possibility of accidentally killing the child (obviously an evil act).
In my view a player should not know the DC for such a task, and furthermore should not know the precise consequences. It's up to the player to imagine the task (I am tossing a warhammer at a running child on a city street from a distance of 30'), and the likely consequences that could stem from that actions failure or success (accidentally kill the child, break his legs, miss and hit a bystander etc).
The player trusts me (as DM) to set an appropriate DC for that task, and to adjudicate consequences for success or failure accordingly.
In my view thats a far better method of resolving actions which better preserves realism, makes players imagine the action more clearly, consider all possible consequences for actions (and not just the ones pre determined by the DM and announced to the player) and not reduce everything to a question of probability.
It also heightens suspense during action resolution which is an important driver of engagement and excitement.
Not knowing the DC/ AC also drives players to use things like bardic inspiration or just normal inspiration and similar effects to push clutch rolls without gaming the DC.
It just works better I find. I dont do it all the time (sometimes it's just more convenient to announce the DC and ask for a roll) but I do do it.