I don't see it as a problem, I think this is the correct idea, and the reason is the holographic principle. The original formulations of string theory were for cases where the background space-time was flat, and in this case, light-cone coordinates seem unnatural. But when you have a black hole, or a cosmological situation, the light-cones bend in such a way that they cannot penetrate through the horizon, and this makes the light-cones a strictly outside description of black holes (when the horizon is a future horizon and the cone a past-cone), or a strictly interior description of cosmology (when you interpret the cosmological horizon as a future horizon, which is not the usual picture).
So the light-cone definition of "now" doesn't have the unphysical extension of space-time into regions where we cannot get signals. When you look at the universe in this perspective, the cosmological horizon is the boundary where the big bang is still happening "now", the horizon was smaller in the past, meaning when you look at the "now" for our past position in space-time, the horizon had a smaller area. The ancient horizon at inflation times was just a little sphere surrounding us, and this picture makes no reference to exterior places, it doesn't have the extended universe of eternal inflation, or of classical General Relativity, in the usual slicing into a 3-d space and a 1-d time.
This perspective is more in accord with the holographic principle, which demands that the interior of black holes (in established formalisms) and the exterior of the cosmological horizon (in ill understood extensions) should be reconstructed from a pure interior description.
So I think this is a better definition in light of the holographic principle, although this is ultimately quibbling over words, the meaning of the formalisms is in the mathematics, independent of which way you interpret human statements like "now" which become ambiguous in relativity.
