I actually prefer DAO's romance system to DAI's romance system. In this one, you have to initiate everything, it feels awkward. It feels as if you are the only one who is capable of having romantic feelings, capable of expressing them and capable of making a move. In Origins, if your companions had sufficiently high approval, they would give you a gift or try and initiate the relationship themselves, which I liked immensely.
This actually makes the romances in the game very trophy-like and turns the potential love interests in the game into something one must attain or achieve or melt as opposed to a two-way street.
Which is something I immensely dislike. I mean if a follower or an adviser is interested in a particular sex and you gain their approval, they should at least give you gifts or speak to you differently.
In DAO, Alistair gives you a rose, Morrigan gives you a ring, Zevran gives you an earring. All of them change their speech pattern as your approval in their eyes increase. Morrigan becomes more girlish, Leliana fumbles with her words, Zevran is more serious and considerate, Alistair more romantic.
In DAI, there is nothing of the sort. It is all up to you, the Inquisitor, to flirt and to romance the character. There is no reciprocation and there is no initiation by anyone but you, the Inquisitor. It turns the romances, at least in the early stages and some even right up until the end stages, very one-sided.