Lets stop complaining about Morgana and recognize the reason she was brought down to the bot lane. When the support changes were rolled out in pre-season 4, we saw three and only three supports. Thresh, Leona and Annie. Annie came to bot lane because of her early game pressure and the ability to out burst Leona and Thresh. All three received nerfs, but Annie was hit the hardest. Braum was then released and took Annie's spot. These tanky supports were able to withstand all poke, while bringing hard/soft CC and sustain through the Targon's line. These supports ruled bot lane. Every. Single. Game. Then, Morgana/Zyra/Nami/Karma all made comebacks due to the buffs to the frostfang line and small nerfs to leona/thresh/braum. These supports were able to bring decent amount of CC, while being able to poke and peel effectively. Morgana was and still is probably the strongest support out of the "poke" supports. Morgana was solely brought to the bot lane to counter these hard engage, tanky supports...and it worked like a charm. Morgana, while being strong, allowed for other supports to be brought down to bot lane. Namely, Janna, Zyra, Sona, Nami and Karma. These supports all do pretty well against Morgana, due to their low CD's and high damage poke. Morgana has a tough time against these specific champions. The support role, as it stands now, is MUCH more diverse than it ever was back in season 3 and early season 4. Morgana was a healthy addition to the bot lane. Lets not complain about her because we want to choose Braum/Leona/Thresh every game. Lets open our minds and play Nami/Zyra/Janna/Sona against Morgana and poke her to death.Some of this is true in the OP but some of it you are a bit mixed up about.
Just a few things were either off or completely wrong:
For example, Braum had nothing to do with Annie being pushed out, not even a little. Annie was gone from the support role long before Braum, and was more Morg that fully pushed her out plus her nerfs.
Braum also wasn't a champion yet when Targon's was a bit...much with people going double Targon's, that was the start of the season not when Braum came out.
Karma is probably the actual strongest "poke" support because of her out of no where burst, along with Zyra. Morg is there for CC and harass ish with her w and her black shield not for her poke.
When Karma came back as popular, for the short time she did, it actually wasn't as support that much outside of the rush combos with Sivir, which didn't last long, more Mid lane and for an awkward and confusing period, Jungle O_o
Again you are confusing time periods because when Karma and Zyra were becoming popular (Zyra was the previous season with Zyra/Ashe bot lane. That was the previous season), Braum wasn't even out yet, and Morg was becoming cemented as popular again, before Braum was even out.
I'm not even sure what you are talking about when you say allowed others to be brought down to bot lane....then name Janna and Sona <_<
.Nami hasn't ever not been support and has been popular for a while, and Zyra was popular all last season, before Morg support was a popular thing.
And to sum it all up, the real and MAIN reason Morg support became a thing wasn't her poke, wasn't even her binding, it was BLACK SHIELD because Leona was becoming like support numero uno and with Black Shield it helped to counter the Leona all in onto your adcs face and everything else in her kit was icing on the cake.
Some of your post was right but soooo much of it was all kinds of bassackwards