Yes, Hamilton was injured. He had a chronic cases of BatsLefthandeditis, which gets particularly inflamed against lefty starters like Fried and Rodon.
Abreu suffers from the same ailment, which is why Eaton got the starts.
No one is saying Sogard is worthless. But even the Sox clearly think Hamilton is better. Both players had options, but Hamilton got much more PT. And even when Sogard saw action, they put him at 1b more than anywhere else, and when Cora needed an emergency shortstop, neither of these two were nigh on Cora’s radar. But Sogard was even further, playing the position for only 5 innings to Hamilton’s 70.
I don’t think they go all Sox themselves are as on board with this evaluation as you are. But hopefully the goal is to push both of them out of the lineup…