As for the simultaneity of two or more events, naked-eye observers placed at arbitrary (non-equidistant) locations would typically come to different conclusions, due to the finiteness of the speed of light. This suggests that inertial frame wide simultaneity is not a direct experience but a mere definition, based on an agreed way of measurement. Similar is true for coordinate time, since it also builds on the concept of simultaneity.
Note: already in the case of duration, two co-located observers need to agree on using an independent device (i.e. a clock) in order to avoid ambiguity.
It does not harm to imagine that the above concepts describe a directly intangible "objective reality" in an inertial frame, but as a matter of fact they are essentially just tools that help us in calculating answers to questions about our (more) direct experiences. The most important question to answer is this: between two events that happen directly to an observer, how much time elapses according to the observer's own clock?