Hmm....it appears I have been misunderstood by some people. I'm no Chantry apologist, and I couldn't care less about what benefits it or not.
The point I wanted to make is that the situation at the well feels like a high-stakes version of the Harrowing to me. Or basically any other situation where a spirit - usually a demon - says they'll give you something really desirable if you let them in. I think it behooves anyone to be very suspicious of such an offer, I just singled out mages because they would've seen such situations before.
So given that there are rather suspicious similarities between a demon offering you something desirable if you let them in, and the Well offering you something really desirable if you let yourself be controlled by Mythal's will, I think any mage who drinks from the Well would be more likely to fall to a demon's temptation and become possessed, which would validate the Chantry's desire for tighter control of mages. And that would be a very bad thing IMO.
What I also see is that some people are caught in the "divine exceptionalism" trap, which goes right along a real-world cultural predisposition for being more lenient towards flaws of a religion just because it's religion as opposed to any other kind of ideology. For anyone actually thinking about this, and being aware of the historical fact that one religion's gods are another's demons rather often, it should be obvious that the fact that an entity is regarded as a god says nothing, absolutely nothing about its motivations and whether or not they're in line with our own, even less so much in line that we trust them to take control of us.
Lastly, about not trusting Morrigan, that is a non-argument. Whoever drinks from the well will not be able to do what they want if who- or whatever holds their leash doesn't want it. Given how Morrigan appears in DAI, I'd trust her over Mythal/Flemeth or Solas/Fen'harel, but again, that's irrelevant. if she drinks from the well, she's no longer in control. and what she wanted or not does not matter anymore if it isn't aligned with the will behind the geas. The question is not what I can do, or will do, with that knowledge, or Morrigan, but what we will be forced to do with it, or prevented from doing.
My main Inquisitor wants that knowledge. It's almost the embodiment of her deepest desires. The price asked for it, however, is not acceptable. One of the very few not acceptable prices she can imagine. She'd have given an eye (that would've been nicely reminiscent of Norse mythology), or a hand, her fertility or her beauty for it, She'd given up the power she had attained as the leader of the Inquisition after Corypheus was defeated with no regrets for that knowledge. Her ability to shape her own fate, however, her individual autonomy, that she will not give away, because there is nothing and no one else she would entrust with it. History, and countless tales, appear to support her suspicion.
Edit:
I can see a very traditionalist elf drinking from the Well. However, I would still see it as unwise. Even a traditionalist elf would know that Mythal embodies both justice and vengeance. The elven gods are all two-faced. Suspicion is appropriate.