I think the problem arose because they didn't make the consequences strong enough in DA2 for using blood magic. We had characters in game, like Fenris and Anders, and characters in books, like Lambert, denouncing its use as corrupt and power crazed, needing the sacrifice of innocent victims and yet both the PC and Merrill could use it with seemingly little consequences. No one ever said to Hawke, "hey why are you using blood magic?" Marathari's death seemed as much due to her own stupidity as to Merrill's use of blood magic. The Tevinter mages hunting Fenris use blood magic and the sacrifice of innocents but then they are portrayed as evil anyway. Apart from some random mage encounters later in the game, where they have enthralled followers and that mage in the Blooming Rose who initially controls your mind, who says it is a combination of blood and desire, you really have no real example of mind control through blood magic. So many people started arguing that there was nothing inherently wrong with blood magic.
In DAO if you want to deal with Connor in the Fade without going to the trouble of calling in the Circle mages, Jowan has to use blood magic and this involves the sacrifice of Isolde. If you do so, then other characters disapprove of this, even if they don't go so far as leaving you for it. If you want to learn blood magic, you do a deal with the demon that involves the sacrifice of Connor's soul. All these things seem far more in keeping with the lore we are given on blood magic, the prohibition against it and the bad effects that result from using it. Even so, they did not really go far enough. Blood mages are meant to be able to control the minds of others. If you did so, surely people would notice and object? When you use the blood of allies to fuel your spells, why aren't they up in arms?
The other problem is the fact that it is meant to involve doing deals with demons for power and they do this because it gives them access to our world. In DAI it is apparently "raining demons". They have unrestricted access to Thedas so why bother doing deals with anyone? Clearly if they did still wish to do so, it is far more likely to involve some form of actual possession of the mage they are doing the deal with or someone else nominated by them - as happened in ME. So this would be extremely difficult to accommodate for the PC and still be consistent with game lore, since clearly the PC would be free to nominate anyone and such a scenario would then have to be written in for every character in the game.
Let's face it the Inquisitor is already going to have a pretty unique power and who knows if there are not others they will acquire that we have not yet been told about, so I wouldn't get too upset about not having blood mage specialisation available to you. I'm pretty upset that Spirit Healer is gone as well but I'll get over it.