Let me cast this in a historical perspective.
As Maxwell's equations came into acceptance there was concensus that light is a form of wave propagation. Maxwell's theory of electromagnetism offers an explanation of how light can carry energy.
In addition, it is already implied in terms of Maxwell's equations that electromagnetic radiation carries momentum in the direction of propagation. However, there was no reason to attribute mass to electromagnetic radiation. Hence there was no reason to expext that gravitation would have any effect on light.
Historically, gravitation was thought of as a force that acts instantaneously over any distance. It was necessary to think of gravitation as acting instantaneous, this had been demonstrated by Laplace. If gravitation would propagate at a finite velocity then there would be aberration effects, and none of those were observed.
Changes introduced by Special Relativity.
Let me first discuss gravitation.
The first to explore the consequences of relativistic physics for gravitational theory was Poincaré. (In 1905, the same year that Einstein's paper on Special Realativity came out.) Poincaré noted that if it is assumed that all theories in the area of mechanics must be Lorentz invariant then a new theory of gravitation is necessary, as an infinite speed of gravity is no longer a possiblity. This new theory of gravitation must reproduce the predictions of Newton's law of gravitation for the known celestial mechanics. Poincaré gave some suggestions on how to develop such a Lorentz invariant theory of gravitation.
About electromagnetic radiation:
Indeed as early as 1905 Einstein had offered a consistency argument that in terms of Special Relativity it is necessary to attribute inertial mass to electromagnetic radiation.
That is: Einstein demonstrated that without attributing inertial mass to electromagnetic radiation you get a self-contradiction. So that is logical implication.
The question that you raise is: does that also imply that we should attribute gravitational mass to electromagnetic radiation? You submit: for matter there is no known exception to equivalence of inertial and gravitational mass.
Here, while a suggestion is there, there's no logical necessity to attribute gravitational mass to electromagnetic radiation. So no: Special Relativity does not imply that gravitation must have an effect on light.
But yeah, there is that undeniable suggestion that gravitation should affect light, and as we know the assumption of universal equivalence of inertial and gravitational mass was among the most important guidances as Einstein struggled to develop General Relativity.
GR replaced SR, and the shift from SR to GR was as profound as the shift from Newtonian mechanics to SR. A fundamental assumption of SR is that the Minkowski spacetime itself is an unchanging, static entity. Overthrowing that: in terms of GR spacetime is not static; there is curvature of spacetime, in response to presence of mass/energy.
Logically, Special relativity does not imply gravitational effect on light.
- Special Relativity invalidates the instantaneous-over-distance assumption that is necessary for newtonian gravitational theory.
- Logically, universal equivalence of inertial and gravitational mass is a separate assumption.