Braum is fine, he's one of my favorite and most solid supports.
Morgana's shield only blocks magic damage and CC, making it far less effective against the enemy ADC (and quite commonly their mid, jungle, and/or top). It also only shields a single target, and can be pretty easily broken as it isn't a huge damage cap.
Braum on the other hand can stop an entire team worth of Ultimates if he times and positions right. He can counter intiations and shut down engages from a huge variety of enemies, and can save his entire team in the process, not just one person.
A clutch Morgana shield can save one person from getting stunned or snared at the right time, but Braum can save his entire team and turn a fight effortlessly.
As for towers, no reason to make it tank tower shots. They're already laughably weak and Braum can tank them himself if he initiates the dive.