That it has critics does not imply it's not widely held. Regardless, that's just a dispute about terminology: sure we could say that we should only talk about

That it has critics does not imply it's not widely held. Regardless, that's just a dispute about terminology: sure we could say that we should only talk about events being "simultaneous" if they happen in exactly the same place - but in that case it's not a particularly useful term anymore. It's just an argument about how we apply words derived from newtonian intuitions to a relativistic context. Mathematically, for a given reference frame we can draw a space-time diagram, and certain events will be above the horizontal line. We can draw the same space-time diagram for a different reference frame and have those same events be below the horizontal line. Whether that horizontal line has any actual physical relevance doesn't really matter IMO, the maths says that events move in relation to the line when the frame of reference accelerates, and that's what the "paradox" is illustrating. Having said that, if the "one way speed of light" exists (https://en.wikipedia.org/wiki/One-way_speed_of_light https://en.wikipedia.org/wiki/One-way_speed_of_light) and even if it's not the same in all directions, then this "plane of simultaneity" is definitely a physical thing, since you can send a beam of light to a target, measure how long it takes to return, and using the speed of light in that direction you can work out exactly when that beam hit the target in your local time - ie. you've found two events to be simultaneous from your frame of reference, that are not in the same location.