I got the impression that the Time Lords were unique, in that they were the first and only race to master the higher order mechanics of the multiverse. Meaning they were the first (and through that virtue, the only) race capable of opening gateways to other dimensions.
They spread out to police the multiverse before anyone else and steered others away from that knowledge for fear of the havok they'd wreak.
So when Gallifrey was wiped out and the Eye of Harmony became kaput, and the Tardises lost the only thing powerful enough to let them skip dimensions, and began having to resort to draining energy from temporal hotspots to keep themselves fuelled for time-jumping.
As for the Reapers - they only showed up because a paradox was created. A few

.