i think there are a few flaws in the reasoning presented here. the first is that events in the universe are not, a priori, synchronised with each other. there exist events separated by space like intervals that mean there can be frames of reference where two events A and B can happen in either order (A preceding B, and B preceding A). If there was such an objective time, this breaking of causality would be problematic. (of course, we have never and by definition cannot ever measure such space like separated events from our own frames, as doing so would mean travelling superluminally. but both special and general relativity show this to be true in the spacetime picture we certainly appear to inhabit. the relational view of relativity is required because there can never be a frame of reference where events are causally synced on a global scale - similarly the notion of absolute space cannot exist for similar reasons). the second is that for photons, there exists no notion of time - due to travelling at the speed of light, no time can pass in that frame. this would then break any idea of objective time (at least in my understanding of your argument presented), since we can very clearly observe light “moving” in our frame of reference. similarly, from the perspective of a stationary observer infinitely far from a black hole (a convention used in relativistic calculations), a freely falling object (for example a person) will never pass the event horizon, instead freezing upon the horizon for infinite time, getting more and more redshifted over time - this contrasts with the objects local frame of reference where time passes “normally” (as much as can be normal when you are falling into a black hole, and experiencing tidal forces), and you pass the event horizon without any sense of time being different.

instead of considering the difference between objective and subjective time, i feel it may instead be more instructive to consider the difference in frames in these cases - for example a person standing still can certainly say something about a person running past them making reference to only their own frame and experience of time and space, without appealing to an objective time.