In General Relativity, the effects on clock rates and rulers have a concrete cause, namely the gravitational field. It's hardly surprising that an all-pervading field can affect the lengths of things or the rates of clocks. One could easily write down equations for other fields that do this same sort of thing.
With Special Relativity, on the other hand, there is no external field causing the effects to moving objects. One then has a puzzle as to "why" the moving objects are affected. The customary explanation is that "spacetime" affects the moving objects, but this just changes to question to why spacetime should affect relativistic matter, when it did not affect Newtonian matter. In fact the difference is field theory, because motion alters the propagation of the fields within the objects, whereas it does not affect the action-at-a-distance forces of Newtonian physics.
Simultaneity is not an issue in General Relativity. In GR there is no concept of the global reference frame for an observer, hence one does not try to extend an observer's concept of "now" to distant locations.
In Special Relativity, by contrast, one has global inertial frames and one can compare different observers' definitions of "now". One finds that these definitions disagree and this leads to the various "paradoxes" such as the twin paradox.
The twin paradox, for example, arises in SR when one incorrectly applies the inertial frame of the "traveling twin". It does not arise in GR, because one doesn't define an inertial frame for either twin. Of course one could, if one assumes that there is actually no gravitational field (i.e., spacetime is flat), but without gravity one is back to doing Special Relativity.
Reason 3 (really a broader way to state Reason 2):
In GR, one is not concerned with comparing the viewpoints of different observers. Rather, one is concerned with calculating the effects of the gravitational field. An observer at point A is affected by the gravitational field at point A, and likewise for observer B and point B. There is nothing more to say about their viewpoints.
In SR, by contrast, each observer has a global reference frame that encompasses the whole universe and all other observers. One then has questions like how each observer can see the other's clocks to be running slow. In GR one never addresses such questions because a moving clock and a stationary clock are not at the same place to be compared.
Again this is a variation on the same theme.
In GR, one is not concerned with measurement. There is no discussion about how different observers measure things, and there doesn't need to be. In studying the gravitational red shift, for example, one doesn't get into a big discussion about how the observers at different altitude make their measurements; the issue never even arises.
in SR, by contrast, one has to deal with the question of how moving observers can each see the other's clocks running slow, and rulers shorter. This means discussing the process of measurement and the effects of simultaneity on it. It is a very confusing aspect of SR and does not arise at all in GR, because it has nothing to do with gravity.
I discuss some of these things further in my book Relativity Made Real,