The biggest problem I see in BR leaders coming to AT is that they want to hurry up and learn all the patterns so they can catch up to the other dancers. It's painful sometimes.
Ampster, too, has in the past often shared his experience coming to AT from ballroom.
And, I as well. Though, AT and Latin are my specialties, I still coach/adjudicate many BR couples/comps. Here is my --very humble-- input....
There are too many variables to make a blanket assessment of the problem. Many things come to mind.
1. Most BR is taught, thus learned, rather poorly. Unfortunately, it is taught as a system of steps/patterns/rules/techs/ and logistics rather than as a living art. It is not the student's fault then that they come to know and dance it as such. This is part of the reason why BR is referred to so often as stiff/rigid/etc. The dancer is dancing, what we call in my studios, "from the outside in"... that is, dancing the rules, and trying to find a feeling from them.
2. AT is the easiest social dance on the planet... because it is one of the most natural movements on the planet. Now, understood, this is also what makes it so difficult. Most of us have, in many factions of our lives, forgotten how to simply accept something for what it is/isn't without any thought whatsoever. In a way, this is natural. We have become adults in an overprocessed world. Another thing that we say often in our studios is, "Approach dance, not with the mind of an adult, but with the eyes of a child". This is to say, don't try to learn, for example, a box step; simply learn to feel a smooth forward walk... that, oops! went sideways, etc. Don't process it mentally as an adult... just do it because it's there, much as a child would.
3. It is this that makes AT what it is. It is not a dance that became systematically inbred into a culture; it is a culture that simply birthed a dance. Now, that dance is as natural in that culture as walking down the street... the easiest movement in the world. It is not a dance of foot placements and leads and follows; it is a dance of natural movments and body positions. As the man moves 'here' his body moves 'like so', and the lady responds. That's it! No more... no less.
BR should (and is in too few circles) be taught as such. These are always the better dancers, and happier people. Sorry if this sounds all too philosophical or metaphysical, but I am convinced that it is where the transition from BR lead to AT lead must begin... by changing one's perception of what BR and AT are. Only then can one change hwo they are done.