So who is voicing Reagan?
The story seems dated. Make it a period piece and it would confuse non-comic fans. Retool it and its not the same, though.
I imagine (rightly or wrongly) that animated movies like this mainly appeal to comic fans and don't appeal to a very wide mainstream audience. I think if Watchmen, a large-budgeted live-action movie, could get away with a setting during an alternate 1980s, where Nixon was still in The White House, then TDKR will get away with its setting and President.
I'd imagine that confusion between this movie and The Dark Knight Rises will prove a bigger problem for non-comic fans.