She wanted to recruit a blood mage Hawke to the Inquisition still, so I doubt it.
Well, given that Varric was her source of information on Hawke, I doubt Cassandra knows, even after DAI, whether Hawke was a blood mage or not. Since, as others have pointed out, there is no narrative reaction in game to Hawke's specialization, it can be ignored unlike Merrill's use of blood magic on the eluvian or Anders' possession.
The issue with blood magic for a protagonist is that it could also be used to skip a lot of quests. Like people have pointed out here, we could use it to force the thane to send her forces to assault the fortress rather than win their trust. We could skip the entirety of WEWH by controlling Celene. It's difficult to provide an overpowering ability like mind control to one class only and then have it have any noticeable effect separate to the other specializations. It's effectively writing a different quest path for one ninth of the specializations.
BUT to actually respond to the OP, some examples I can think of:
force the Hand of Korth to stand down rather than fight him to the death. Have him join his tribe to the Inquisition.
Use blood magic on all judgements to either get them to reveal information (Alexius, Samson, Denam, Erimond, Servius) or to ensure their loyalty (Florianne, Alexius, Servius).
"Convince" the Dalish clan you're their friend rather than perform tasks.
Control the Blades of Hessarion leader rather than duel him.
Have a special dialogue option in Dorian's personal quest, which may lead to him automatically leaving the Inquisition
It would be cool if we tried to use bm on Denam or Alexius during their quests but they were protected from it by red lyrium.
Try to bind Imshael to us or strike a better bargain than what he offers.
If we want to be really evil, during IYHSB have the option of sacrificing the townspeople we're supposed to rescue for a temporary power boost or refresh of health.
I think one downside to blood magic should have been that it takes two more waves of demons to close rifts, since Solas says it makes interacting with the Fade more difficult. That would outweigh a lot of the shortcuts it provides in quests. And maybe have some effect in HLtA when we're in the Fade, like a slow but steady loss of focus or stamina/mana.