The Alice and Bob example is meant to portray the argument for maintaining confidentiality between the commentators and the trials. The former case is still a potential problem, because of the assumption that other people have proper arguments for why Bob shouldn't be a GM. This isn't necessarily true: perhaps Alice has an IRL (or at least external to Toribash) relationship with Bob that provides her specific information on why Bob shouldn't be a GM that no one else in the community should have. This would, at first glance, seem really uncommon; but it has happened before.
I'm perfectly willing to accept that that specific separation isn't really a good idea in and of itself though: certainly, it'd be exceptionally hard to enforce on a technical level (What's to prevent a trial from creating an alt and reading the supposedly publicly available thread that way?). If we're going to have public commentary on the trials, it might as well be open to them as well.
Private commentary on the trials is already possible (though exceptionally infrequent), and I don't feel that it has been exceptionally unsuccessful.
I'd be perfectly happy with opening another discussion on whether or not the GMs as a whole are performing adequately to the community: This has been done in the past and has traditionally been at least somewhat helpful. Furthermore, the GMs have already been given their positions in full, and the comments on the GM team are generally not directed at individuals. Traditionally, individual complaints have been dealt with in Complain About Staff (which is currently where publicly listed complaints about trials would go anyways, under the current system; preferably after contacting the trial in question specifically).
I think the single largest complaint about the system your proposing comes from potential abuses of it. It is extremely common in voting systems with anything resembling actual consequences to put as little trust in the user as is possible to do so while still getting a useful result. This is not because we don't trust any one particular user, but that there's always the possibility of at least one particularly malicious user who wishes to take advantage of the system. You cannot design secure systems if you willfully overlook that potential malicious user.
Thus, in short, the system would appear to be abuse-able by a malicious regular user in the sense that there are methods by which to present relatively benign situations in extremely bad light. While such complaints are, of course, already possible; opening up such complaints to a discussion intended for this sort is probably not going to result in the kind of thread you had in mind. I'd really expect it to devolve into flaming or trolling, which would be extremely awkward to deal with, since a thread like this would also likely have a "We won't ban you for calling people idiots in this thread" sort of clause.
From the side of a malicious trial GM, there's enough stuff on that side as well. "If you help me get full GM, I'll do <X>" and whatnot becomes potentially possible. If it's done cleverly enough, it's possible to even deflect potential corruption reports if those sorts of things do come up. With the current status of the community having no positive say on the trial->GM progression, this is actually completely impossible; and the GMs have already been selected in a fashion that makes any one of them particularly unlikely to allow this to happen. The same cannot be said of the general community.
In short, I get that you want to assume that community is great and helpful. It's even, more often than not, true.
When it's not true, however, unless you've designed the systems to tolerate it not being true, everything breaks. Usually it's really dramatic when that happens, and the cleanup occupies a really significant amount of a decent amount of the staff's time.
As such, these systems should be designed around the concept of not that "Nothing will go wrong", but rather that "Nothing CAN go wrong". Not because placing trust in the user base is a bad thing, but because if it's misplaced in the user base it can turn into a real shit storm if it's not managed properly.
In this case, I feel the current system of trials works (quite) well, and that this system is likely to provide more potential and incentive for abuse if any particularly malicious user exists who wishes to take advantage of it. If you can show that it does not provide the potential for abuse, then there's really no problem at all with opening such a discussion.
I do also agree that the user base needs to be trusted with the ability to comment on the GMs: the GMs, as a whole, are definitely there to help the game be enjoyable by everyone in the community. Thus, any member of the community should have the right to comment or criticize their procedures (within reason, of course). To a similar extent, everyone has a recourse to complain about staff members they have grievances with in Complain About Staff. However, I do not feel that actively trying to involve the community at large in the Trial progression process will result in a better Trial progression process.