I like to think that the rift energy allows the Eye to be kept accessible. Remove the rift energy and the power provided by the Eye can't be transferred to the engines. (It's strange that the question of rift energy wasn't addressed in Journey To The Centre Of The TARDIS.)
It's not strange to me at all, since the Rift was an RTD concept and it's Moffat's show now. Moffat has taken the show in his own direction and has rarely brought back any story elements from the RTD era.
has never been a franchise known for strong continuity or internal consistency. The specifics get reinvented all the time, so it's wisest not to dwell on them. It's best if you look at it in a more impressionistic light, or as an epic myth. The details of a myth change depending on the teller and the era, but the essentials remain.
But if you want an in-universe explanation, keep in mind that a couple of more centuries have passed for the Doctor than for us. And didn't the Cardiff Rift turn out to be one of the cracks in time or something? Wasn't it closed several seasons ago? So the Doctor would've needed to find a different power source, and would've had plenty of time to figure out how to access the Eye.
Since the Doctor said in The Lodger that the makeshift TARDIS could destroy the solar system if it exploded, and since he said in Blink that the Angels could draw enough power from the Doctor's TARDIS to switch off a sun, I think it's reasonable to say that the star from which the Eye Of Harmony was created was at least as massive as the Sun.
Well, that's a given. Stars don't collapse into black holes unless they're at least 30 solar masses. A Sun-size star would just expand into a red dwarf and slough off its atmosphere as a planetary nebula, with the core becoming a white dwarf.