Crunchyroll is owned by Sony now, and yet there is no such offer with PS+.
When there were rumours of tiered PS+ coming, people were thinking maybe it will have subscription of Crunchyroll or funimation (also owned by Sony), but nope.
I did not know that, It is pretty humorous. You would think they would want to use it as a draw. Especially since they're huge in Japan where anime is king!
Couple of things that I can think of, first Sony is a conglomerate, and different parts act completely independently from each other, so there might be some other stuff needed for such an agreement, that PlayStation side didn't care about.
Second, PlayStation has started focusing on west much more than Japanese side. PS headquarters has moved to US, and all the top level people are now western people. Japan Studio was also closed, and only one team remain from that. All this shows that they are focusing more on western audience than Japanese one.