Doing so would be a 'disservice' to the game
One can only imagine what goes on in the BioWare forums on a day-to-day basis, but thankfully, the highlights always seem to find their way to us. Community manager Chris Priestly wrote a post saying "To call the next game Mass Effect 4 or ME4 is doing it a disservice and seems to cause a lot of confusion here. We have already said that the Commander Shepard trilogy is over and that the next game will not feature him/her. That is the only detail you have on the game."
Continuing, Priestly said "I do not call the game ME4 when I talk about it ever, because that makes people think of it more as 'what happens after Mass Effect 3' rather than 'what game happens next set in the Mass Effect Universe,' which is far more accurate at this point."
Picking up where this conversation left off, more recently, BioWare Montreal studio director Yanick Roy offered up the following insight: "What Chris is saying is that thinking of the next Mass Effect game as Mass Effect 4 would imply a certain linearity, a straight evolution of the gameplay and story of the first three games. But because we are switching to a new engine and need to rebuild a bunch of game systems, we have an opportunity to rethink how we want these systems to be going forward instead of just inheriting them from the previous games.
"Story-wise, the arc of the first trilogy has also been concluded, and what we will do is tell a new story set in the Mass Effect universe," he continued. "That doesn’t mean that events of the first three games and the choices you made won’t get recognized, but they likely won’t be what this new story will focus on. In other words, because the game takes place before of after the first trilogy does not mean it necessarily is a straight prequel or sequel."