While the light speed invariance appears natural in AWT, the concept of dense Aether explains, why it was so difficult to understand it even for Aether proponents. The trick is, the inertial energy spreading always follows the surface of energy density gradients, because of highest local density gradients, which are slowing/mediating every inertial energy spreading.
This can be understood easily by using of surface water waves example. The fact, most of energy spreads along the water surfaces in transversal waves doesn't means, the energy cannot spread through air or underwater in longitudinal waves - on the contrary. During shallow water explosion most of energy will spread
through air and underwater shock waves. But the energy density of these waves will be quite negligible due the low volume fraction of water surface. This is because the water is rather incompressible fluid, while the air is compressible enough, but it's density is rather low with compare to density of water. By such way, the surface density gradient of water is the place, where the energy can spread by the lowest speed and the energy density of explosion is much more pronounced here, so just the surface waves are having the strongest devastating effect. From surface observer perspective, the effects of both underwater, both air waves are rather negligible - the main portion of energy will spread in surface wave.
And this is the key in understanding of transversal nature of light. As I explained above, the vacuum can be considered as a dense system of energy density gradients, similar to foam. And most of energy will spread along surfaces of these gradients, i.e. along strings and membranes, forming such foam at the distance in transversal waves. The portion of energy, which will spread through bulk of such foam will remain negligible the more, the more pronounced these gradients will be.
From the above follows, because of high vacuum density, most of energy will spread through it in transversal waves and the longitudinal portion of energy spreading (the gravitational waves) will remain completely negligible with compare to the transversal one (the light waves). Furthermore, the longitudinal waves will disperse by foam membranes fast, so they will remain difficult to detect at large distances. Therefore the Aether foam model explains the transversal character of light waves and it even brings a new insight into contemporary problem of gravitational waves detection.