The choices here are to either make your PC break the "don't put that in your mouth" rule or push it onto a convenient NPC. Why is that a hard one?
The characters I play are usually a little too risk-averse to be willing to consume an ancient unknown substance with unpredictable effects.
This decision made me flash back to DAO with my Female Mage Warden's dark path where Selena was literally drinking everything offered to her for more power and murder kniving everyone...good times.
I didn't murder knife but I sure slept around. And I was torn on drinking the weird magical blood, but was I a power hungry Cousland who'd become Queen of Fereldan or wasn't I? 
CHUG
Morgan or the Inquisitior
That is what I thought at first, but then listed it mentally as a typo.
Only my Dalish characters drink it.
^The (ex)Inquisitor who drank will send your new protag a text message about it.
Morgan or the Inquisitior
I only see a 404 error on the first image, so I don't know the context of the joke.
Anyway, one thing that always bothered me about the Well choice, why is it that you can only ask mage companions if they would drink? The Inquisitor doesn't need to be a mage to drink, so why can't you ask Cassandra, Varric, Sera, Cole, Blackwall, or Iron Bull if they would drink?
I could see the Inquisitor turning to Bull, smiling and saying "Maraas-Lok", and then Iron Bull says, "Ehhhh no thanks boss. The only spirits I drink come out of a bottle."
They didn't want to track the possibility of Sera having a heart attack and dying when you asked her, that's why.
They didn't want to track the possibility of Sera having a heart attack and dying when you asked her, that's why.
Morigan because then she is bound to her mother and/so Solas.
I'll admit, I do find the irony of her being bound to mommyMythal almost too delicious to pass up, but my elf mage quizzies refuse to budge.
In spite of thinking that it's a much better idea to give it to Morrigan, I will concede that I had my Dalish elf mage drink it for about the same reasons Tidus's was going to, which is probably the same one yours would give. (My argument as far as the "don't put that in your mouth" rule was about what the Inquisitor would be smartest to do, not whether or not any specific Inquisitor would do the smart thing.)
My Lavellan would have shoved her out of the way to drink it if it came to that.
The rest let her have it.
Seriously with all the Mythal things going on I can only see this as huge-impact-material for the next game.
So.
I'm going to do both runs with the dalish solasmancer lavellan. To be ready if it ever gets relevant.
At least I can read all the dialogues I guess
That's more or less the reason that I don't expect I'll ever have an Inquisitor drink, with the possible (perhaps probable) exception of a Dalish mage.
The characters I play are usually a little too risk-averse to be willing to consume an ancient unknown substance with unpredictable effects.
Funny enough, any Dalish character I roll would never touch the thing (but then, all my Dalish elves would be imperialist renegades, so...). I did have a human who drank - devout, so the idea was that regardless of the geas this was one more burden from the Maker to bear.
They didn't want to track the possibility of Sera having a heart attack and dying when you asked her, that's why.
They cover this, but you have to be a mage.
I choose to have my Dalish Inquisitor drink from the well for numerous reasons: one of them was that she was not sure if she could trust Morrigan including that she would not leave, that she would not withhold information and how she intended use whatever she learned.
The meta reason was my curiousity to see what would happen if the player character drank from the Well. Morrigan being denied something was a bonus. I should note that I do like Morrigan.
It's funny that Cassandra disapproves if you let Morrigan drink even though she says to you that if it is truly between you and Morrigan, you should let Morrigan take the risk.
The Inquisitor doesn't have to be a mage to drink so why should it be necessary for anyone else? Does the green glowing hand make you an honorary mage?
Still I doubt it would be worth suggesting it to any of the non mages anyway. Cassandra wouldn't drink on principle. Iron Bull would think it too much like demon s**t (and if he is still in the Qun why would you want them to have it?), Sera's reaction would be unprintable, Varric wouldn't go for it and Cole was advising against it because of the voices in your head. The only one who might conceivably agree would be Blackwall but I think even he would be wary of it. So it would have been a waste of time and resources to offer it to all companions.
My elves drink it and my humans let Morrigan.
I almost laugh now at Solas' reaction if you ask him to do it after playing Trespasser. He sounds so desperate and now I know why
Do góry