Setting up a Mathematical Institute of Refereeing? This question is mainly focused on the field of mathematics, although it might make sense for other areas too.


  would setting up a Mathematical Institute of Refereeing be a good idea ? 


To explain the idea, I have noted several things that seem to go in the same direction :


referees today are not paid for their work (at least by good quality journals, I'm not talking about predatory ones), they do it by goodwill to be active members of their communities ;
discussing a result with a colleague always speeds up one's understanding ;
in many cases it is difficult to find a referee for a paper, and the process can easily take 9 months just to get a first report ;
many people experience a draught at some point in their career.


So what about an institute where members have a temporary affiliation (say a 5-year contract, which they can quit at any time) and are tasked to only do refereeing, any involvement in other time-consuming activities (teaching, grant application, but also one's own research) would be banned (and checked regularly by the administrative staff and citizens). 

The members would be sworn to secrecy (like a medical one, with cash and jail sentences if found guilty of breach, say during their membership and the 2 years beyond it), which would allow them to discuss papers they are reviewing with other members on-site.

Funding would be provided by a variety of sources (Universities, Private sector...).

And to make sure that there is no change from traditional anonymous refereing, these referees would not mention in their report that there are members, so it would look like it had been done by a standard referee at a university (but much faster).

The idea would be both to speed up the process, and to lower the pressure to publish mediocre papers (i.e. it would be valued more highly by the community to know that someone is a hard-working member of that institute, rather than someone is painstainkingly publishing small papers every couple year which consume refereeing ressources while adding little value to the area).

[edit: thank you for the answers and comments, many good points there of course. Clearly not all sub-fields of maths would be covered this way, but I thought it might help in some where this is high traffic. Plus, I thought people towards the end of their career, who have taught for 25/30 years and, in some cases, have also lost a bit the will of finding new stuff all the time, might be interested. (If you don't find it lacking courtesy, I think I'd like perhaps not to accept an answer to let it open-ended.)]
I'm an assistant professor of mathematics and while I regularly referee papers (in fact, I have a few papers I'm supposed to be refereeing right now), I have to say that joining a Mathematical Institute of Refereeing sounds awful. It's right down there with joining a Mathematical Institute of Departmental Meetings. 

Perhaps it's just me, but the aspects of my job that I love the most are being able to teach mathematics to and mentor talented students, working alone or with collaborators on research projects, and writing up / publishing papers. Although I definitely get something out of refereeing papers (and seem to referee ten or so a year), this is mainly something I do in order to be a "good mathematical citizen". That is, I expect that when I submit a paper it will be competently refereed, so it's only fair that I referee the papers of others when I'm qualified and able to do so. There's no way I would give up all of the aspects of my job that I love in order to focus full time on refereeing. (If such a thing were even possible. I'm not sure how my college would react if I told them that I'm going to be refereeing papers full time for a while but will be back in time for the Fall 2024 semester.) At the end of the day I think what it boils down to is this. I also enjoy doing yard work. But I'd never consider quitting research and teaching in order to focus on it full time.