They did... There's only a small live team and a small developer core working on Destiny 1 and follow up DLC. Most of the focus is turning to the second installment.

You have no idea the amount of backlash that will occur on that day. Lets say September 15th, 2016 Destiny 2 comes out. Due to the terrible PR of telling when bad things will happen and avoiding problems till they arrive, Bungie PR will do all it can to ensure such information does not come out. If anything, There will be a sudden and swift pulling of the rug from beneath all players of base Destiny, only for them to turn around on their first weekly update and say that Activision has decided to take down original Destiny servers. or that they cant support 2 games worth of servers. All in all, it would be a terrible idea to get rid of Destiny as soon as Destiny 2 came out. This is activision we are talking about, so the most likely thing they will do is keep up the servers up until the moment that they are getting no money from it, or if they need more space for Destiny 2 servers.

They did, but while there is still DLC to come, the developers will still be working on Destiny (1).