I'm all for research papers being made more open and available, rather than hidden away through paid-for journals --- this is in my opinion one of the worst parts of how knowledge is shared. However, I'm not sure that making the papers actually able to be modified through a platform like this will make research more accessible or authentic, at least without changing virtually everything else about how science is done in academic institutions.
If the content of a paper changes over time, it becomes more difficult to reference that paper. You now have to include both the paper and something which identifies which version of the paper you read. This is possible of course, but is a fairly big inconvenience for mostly stupid reasons, such as various citation styles not allowing hyperlinks of any form. There is also the possibility of the content of a paper changing completely, though we should hope that people would use a tool like this sensibly and it wouldn't be an issue.
This proposed platform puts a burden on the authors of the paper to maintain a paper indefinitely. Of course, any paper you author you are at least partially responsible for, and any legitimate errors should concern you. However, having to keep up with many comments and/or critiques after a paper is published would be very tiring. The metrics by which academics are measured for their employment are heavily biased towards publishing a lot of papers, and having to spend a lot of time curating old work would be detrimental to anybody's career. (These metrics are also a reason that people would rather write a new paper to build on the old, rather than incorporating it into an existing work). Another issues is papers with many authors: do they all need to agree on a change to have it merged? How often do you want to try to contact 10 people in 4 different timezones to debate about minor changes to old research?
I also don't really understand how a system like this would address the problem of fraudulent papers in a better way than is done today, which (as far as I am aware) is academics contacting journals to get the papers retracted.
I don't think it's a bad idea, but it is so far away from how people publish today that many things (journals, metrics, work loads) are against you.