Three factors characterize papers
I think what is wrong with the publishing system is different to what others complain about. From my perspective the main problem is that it confounds three things.
1. Truth - each paper has a truth value associated with it. Is it significant? How p-hacked is it? Will it generalize?
2. Innovativeness - to which level does a paper break new ground? Opens up new avenues?
3. Relevance - who relates to the message of the paper?
The “profile” of a journal mixes these three things together and glamour journals heavily overweigh 3. But these points should really be evaluated separately. A few examples:
A glamor journal is defined as a journal that is read by many people and hence cited by many people. So it goes for relevance. As it should - and it is good because it provides visibility for good introductory papers to the field.
The problem is that given the way the system is organized it is very hard to distinguish the huge number of mildly relevant papers that are bad on both truth and innovativeness from the small number of truthful, innovative papers that are just only relevant to a relatively small number of people. I do not see how post publication peer review or any of the other factors would really improve this problem.
Counting citations is just as bad, readability will almost always trump innovativeness.
One example of the problem is the following. Assume someone develops a new technique (very innovative) and writes a very math heavy paper about that (not relevant/readable to most). In a non-glamour journal. Now, a bunch of people build software packages to analyze brain signals. They write a few easily accessible articles in glamour journals which get lots of citations. The person who invented the method as well as the journal they published in will look far weaker than those that popularized the method.
I think it would be nice to build a journal around these ideas.