Right now, I am outside the academic system, so obviously I only speak for myself, plus based on my knowledge from many years ago. Maybe the whole process has changed drastically - so please correct me if things have changed.
Even today, every single piece of publication already has multiple choices: a) be uploaded as an unreviewed PDF on the authors' websites - this grants the paper absolutely no credibility obviously, except it may have been written by a respected authority - and definitely you get no benefit as a researcher b) be sent for review, become subjected to copyright, but on most occasions where an unformatted (i.e. preprint) can be uploaded on the website with the express understanding that no one would ever cite that version because it is possible for content to change from that version to the final print version and c) be sent for 'stamping' as the authorized final version, at which point the trouble usually starts.
As you progress along each step, you are basically getting additional benefits - they are somewhat intangible, but for researchers these benefits do translate directly into the currency that they care about - acknowledgment of their work as a part of the citation graph (which then translates into career benefits). So no, the commercial publisher does not "reap all the benefit of this authority and brand value". The commercial publisher does reap all the tangible monetary benefits of course.
Very few authors would willingly submit themselves to the painful process of paper review if they felt someone else was getting ALL the benefits.
Your question could be phrased as whether the publishers get an unfair share of the benefits - yes they do. And do they use some strong arm tactics to preserve their ability to get gobs of money for effectively very little work - yes they do.
And "couldn't just the same thing happen with non-commercial free open access journals?" I think it will, I just feel the road will be quite bumpy until we get there.
I will assume for a bit that the vast majority of participants in the review system are academics. So, one of the main reasons the publishing process moves at glacial speeds is because many reviewers are time constrained academics. Nothing in the open access process will change that fact, but many people will be affected by the shift to open access - suddenly you don't even have an organization that can be held nominally accountable for speeding it up. Academics very rarely like being told what to do, and at the slightest sign of dissent against their handling of the review process, are more likely to stop contributing their efforts towards organizing because the rewards are not very tangible.
The OSS ecosystem faces similar issues and still gets a lot of work done at impressive speed - but remember that usually the top contributors in OSS have immediate positive feedback in terms of the adoption of the software (at least) but often much more tangible benefits such as acknowledgement of their efforts in public and VISIBLE forums, sometimes even employment. Very little of this is true for participants in the review process.
As I said, I expect the road to be bumpy.