Let's suppose for a moment that Telltale decides to cast the player among a new band of survivors in the next game. If the survivors stumble across any plot threads or characters left over from the previous five episodes, the player would be privy to information about them the PC within the game wouldn't.
For example, the new group happens to bump into Lilly. Depending on how Lee left her, she could be living a semi-feral existence in the woods, or using the stolen RV as her home. The new PC wouldn't be sure if Lilly is trustworthy, but we (the player) would know for certain that she isn't trustworthy, based on her actions in the last game.
The easiest solution would be to have Clementine as the PC, but as other forum members have pointed out, this has its own set of creative challenges too.