"All they needed to do was put a more modern, emissions compliant drive unit in the thing. There are a lot of them out there, even from their parent company."
It's not emissions. I mean yes, they would have to eventually - but the current unit has been running a lightly modified Puma engine from the Transit. The Transit will need a new engine in 2020, as will lots of other vehicles. Emissions aren't the reason, but they're another embuggerance that has made "now" the time to do it.
The specific reason it is going in January 2016 (and not 2020) is that as of next month new regs come in on airbags and general safety in commercial vehicles - they gave Defender a stay of execution when those regs came in for cars by reclassifying it as a commercial vehicle, but it's caught up with them.
You can fit a Series II door into the Defender frame, which tells you as much as you need to know about how much the bodywork has been updated over the decades and how much thought went into fitting such niceties as airbags (which didn't exist back then!).
They couldn't export to North America, and so the time had come to build from the ground up a new vehicle which could be exported globally and made with modern manufacturing techniques (not 3 guys with rivet guns fabricating the rear tub from a dozen separate panels when a modern design could be stamped in a second by a machine).