On the contrary, I would say that the Lorrentz transforms prove that time is fundamentally different from space. They form a continuum in some sense, but they are not the same at all: you have to flip the sign of the "time" coordinate compared to the three space coordinates to get the right results.
Additionally, events in 4D spacetime can be either space-like separated or time-like separated, and this difference is the same for all (inertial) observers.
This is especially relevant in discussions about the arrow of time since all inertial observers agree on the order in which time-like separated events happen. So even though in the 4D spacetime model there isn't an absolute ordering of events, there exists a partial order that all (inertial) observers agree on.
Yes, there is always a 1D time aspect, which is always different than a 3D space aspect.
But relative to two observers traveling in different directions at relativistic speeds, the way time is observed to be oriented in a space time region (where the two observers directions of motions are not parallel) is different.
Different to the point that orders of events (their observed direction of time) can be completely flipped.
Upon smoothly changing the angle of one observer A’s motion, from parallel to the other observer B, to orthogonal, to reverse parallel, the observed order (observed time) changes.
A initially sees the ordering as identical to B’s, then simultaneous (no time between events, I.e. time is orthogonal to the space-time vector between events: space-time delta vector of all space, no time), then in reverse order (negative time orientation, relative to A’s observation of time).
They both see time, different than space, but its direction through space-time is observed to be in a different direction in space-time relative to each other’s observations of the same space-time position’s of events.
The orientation of time through space-time, the space-time basis vectors, change based on observation.
Between observers, space & time get traded off with each other.
But only upto some limit. Events that are timelike separated are always perceived to happen in the same order by any two observers. It's only events that happen farther away in space than in time from each other that can be perceived in different orders.
So, I don't think the relativity of simultaneity hurts the notion of an arrow of time that much. You don't get a single universal arrow of time, but there are still local arrows of time all over the place, ones that all observers agree on.
Additionally, events in 4D spacetime can be either space-like separated or time-like separated, and this difference is the same for all (inertial) observers.
This is especially relevant in discussions about the arrow of time since all inertial observers agree on the order in which time-like separated events happen. So even though in the 4D spacetime model there isn't an absolute ordering of events, there exists a partial order that all (inertial) observers agree on.