TLDR
...There was nothing stopping her from just giving it to Leliana*the other "official" candidate* or simply dating the Inquisitor in secret like Lel does with the Warden.
She chose not to do either.
Again her choice.
As mentioned above, it's deliberately left ambiguous. There's a few points to consider here:
1) It's not clear that, as a lay Divine, Cass actually has to be celibate, personally. Since she's not a mother of the chantry, she hasn't taken that vow. Maybe the Divine has an extra vow of her own. But maybe there's just the unspoken assumption that a lay divine, like an ordained divine, would be celibate.
2) It is pretty obvious that being in bed with the inquisition could cause political problems for Cassandra/Victoria as she tries to reform things. Sure, the inquisition is popular with the people of Thedas, but it has a lot of enemies within the chantry. Also, Cassandra's relationship with the Inquisitor could be used to de-legitimize either of them -- was he just a puppet that she established? Was she being manipulated by him? These are Orlesians we're talking about. The simple truth that two of the most powerful people in Thedas love each other would strike them as silly.
So, bearing those things in mind:
-Cass is extremely dedicated to doing what it takes to reform the Chantry.
-Cass mostly seems to have ordered her life about doing the right thing rather than the thing that makes her happy. I am not sure this changes even as she gets more friends, finds love and hangs around losing to Varric at cards.
-Cass is -also- a passionate, hopeless romantic who has twice gotten involved in romances that would have been at least mildly scandalous. She brings up the implications early on in her romantic arc, but it's clear that she gives zero fucks and has no regrets once things get going. And she never expresses regret about getting together with Regalyan. It's obvious that the added political dimensions of being Divine weigh on her, though.
So we have a lot of factors pulling in a lot of different directions. And that is why I could see this going either way. Strict duty to her mission of reform would demand she break things off with the Inquisitor; and she believes that reform is divinely ordained, albeit with qualifications about not actually knowing the Maker's will etc etc. On the other hand, I feel like Cassandra was happy in Skyhold/on the road in a way that she might have never been in her life (and not just because of the inquisitor). And maybe having been happy, she will be less likely to give herself to her duties without reservation.
Edit: as a final note, I can't picture Cass settling down with the Inq regardless. She has too much stuff to do, so I'd imagine any continued relationship (even if she was not divine) would consist of occasional visits when her busy life allows it rather than say, moving in together. I feel like the most happily ever after romance is Cullen.