The core is just as inefficient as it's always been (it's still a simple turbojet in the middle
You seem to give the propulsive efficiency a 5 star rating while the gas generator efficiency barely gets 1 star above.
The 2 efficiences go hand in hand as continual improvements in both have brought about an ever declining sfc since the day after the first jet entered service.
There's a lot of intense stuff going on in a GE90-style gas gen in terms of temperature and pressure at levels far beyond those in an inefficient machine of a bygone era. Those levels are not for nought. They are required to meet the power absorption demanded by that size of fan.
The pressure ratio and turbine temperature are only 2 of the things that go into defining the gas gen efficiency. So its improvements in all those factors which mean an old turbojet core just doesn't get a look in any more for any application.
PS On reflection I think I have just got Adam's meaning, ie not that the core is inefficient, but that todays core, if used in a turbojet at subsonic speeds would have an inefficient propulsive eff despite a much-improved core eff. Silly me and apologies to Adam.
I guess my post really deserves deleting but I'll leave it in case anyone else misread the original.