It would probably save a lot of bandwidth, and make the game smoother. I'm not sure if Minetest already has it, posting anyway.
Now, if both server and client calculated the movement, much like in the old Quake 3, then the client would just send the server for example, starting and ending points. Then server would check if they are the same as the ones it calculated, and if they are not, it would send a signal to the client, which would make it recalculate the movement. If everything is ok, the movement happens. You can check Quake 3's system if you wish.