Is research a viable business model? I have had the suspicion that it may be for a while and apparently not all is a product of my mind. Let me quote from an answer:


  In my experience, in UK and other European countries, the research
  funding comes from successful proposals to the relevant funding
  bodies. There are research centres that were established and keep
  going only because the staff there constantly submits project
  proposals (somebody told me that the success rate is 1 out of 5 or
  maybe even lower).


There are two questions here.


Can a company feasibly focus on obtaining funds in publicly funded research (as a business model) successfully enough to "survive"?
Can such a company be started (nearly) from scratch?


In short, the company would be exactly like a research institute (or institution) except that it would be private.

Reasons why question 1 may not be feasible:


I don't see any company doing this kind of thing, i.e. there may be some, but there are not many, which means that it may be hard. It's a bad sign.
Public funds seem to be assigned to public entities, while companies can benefit from the collaboration and synergy, but they are expected to get their funding from their work as companies (searching for customers, etc.) In this case the customers would be the partners in the projects and the society itself, but again, this seems to be an "innovative" (maybe naïve, or even plain stupid) idea.
Research is a means for something, not an end on itself, that's why the business model should be on something else (point two) and that's why such a company would raise eyebrows on the mere idea of its existence. It may even be against some kind of tacit rule or even written laws.


Reasons why question 2 may not be feasible:


No previous history of success of the company, or products or anything means zero (or negative) trustworthiness and no projects assigned to the company.
No partners would like to associate with the company in a project for the reasons in point 1.
The most similar case I can think of are spin-off companies that are created from successful research labs, not from scratch.
OMG so much communism! Go to kickstarter you hippie!


As an example, a possible scenario that could be close to this: Someone writes a paper about a software system that does something not very novel in the state of the art but in a way that is very different from an architectural point of view, leading to good results in practical terms. In short: in theory nothing is new, in practice what was just a dream is now a reality. What is done remains the same in theory, but how it is done is completely different in practice (and now it works). Unfortunately only a proof of concept (PoC) can reasonably be implemented.

Would it be feasible to request funds to continue the development of this PoC (still very far from a commercial product) as a start-up or that simply doesn't make sense?
In Europe, companies exist that primarily live from FP7 or, now, H2020 funding. They rarely contribute much to projects in terms of research, but often handle tangential issues, such as project management, dissemination, marketing, or association with standardization bodies. Their model works because (1) they do things that none of the research partners actually wants to do, and (2) because they are often SMEs, which is generally politically helpful to get your funding proposals accepted. Further, as writing grant proposals is their core business, they usually also have grant writing experts that have the time to actually keep up with the various changes that the european commission is constantly applying to its programmes and rules (something that many researchers struggle to find the time for).

Formally, these companies often camouflage as either consultancies or technology spinoffs. That is, you will not find it on their web page that their core business model is actually to milk grant programmes, as this is strictly against official funding rules (as a company, you can only apply for funding if you plan to commercialise the results, and you are not supposed to make a profit from the project itself). In practice, the project officers seem to tolerate these businesses - for now.


  Can such a company be started (nearly) from scratch?


You will need a reasonable amount of seed money, as the H2020 rules require proof that an organization applying for grants has enough financial stability to likely survive over the typically 3-year project duration. I know from one startup that wanted to participate in a project (for actual technology reasons) which was in fact struggling to cross this hurdle. However, if you have the required seed funding, I see no reason why you would not be able to start such a business. Whether it is a smart business idea is a different question, given that you are basically living off of a loophole in the current funding practices, and you can never tell how long this loophole will stay open.

Edit:

I just saw that I missed this question:


  Would it be feasible to request funds to continue the development of this PoC (still very far from a commercial product) as a start-up or that simply doesn't make sense?


Yes, at least in Europe there are funding sources for exactly this kind of case. You should inform yourself about the concept of Technology Readiness Levels (TRLs, slide 4), and the different kinds of funding available for each TRL. If you look at this presentation and go to slide 32, there is an overview over different funding instruments in H2020 depending on the maturity of the idea.