Because no one wanted the job, even Southgate seemed reluctant at the time. It's easy to forget that the team Hodgson/Allardyce left behind was pretty shit, and most of England's best/most exciting players have emerged over the past 6 years.
Edit - On that last point, looking at the current England set up, I'd say only Walker, Henderson, Sterling and Kane were playing a regularly and at a level good enough for England when Southgate took over.