Can I write a paper out of a simple idea?
I like papers about simple ideas. (I am writing one right now, hope others like it as well.) They are far easier to communicate and understand than complex ideas.
Then again, the question is why nobody else has thought about an idea if it is all that simple. In your specific example, the idea may not be workable, because people may simply delete the update SMS without replying to it. (And those that do answer may not be representative of your sample as a whole.)
So I would say that writing a paper about a simple idea is good, but it needs to meet the same conditions as any other paper: it needs to show that the idea actually works. An idea by itself is usually not worth an entire paper. Having the idea is often the easy part. Showing that it works is where the actual work happens.
So: Build your website for one city, let it run for six months, then write a paper about what you learned.
How to show that something "works" may well be the hard part. (For instance, in some parts of machine learning it is easy to "show" that a method is better than an established method by testing both on many datasets but then only reporting those on which the proposed method is superior.) Some journals/conferences/reviewers may be more stringent about what they consider proof that something "works". You may be able to get a publication out of a proof of concept by just building the website, without running it productively. Or by running it productively, but without assessing in some way whether the statistics collected by the website are actually more accurate than those collected in some other way. Look at what kinds of papers your target venue or community publishes, and let yourself be guided by that.
EDIT 2016-04-07, about that article based on a simple idea: it turns out that this simple idea (a randomized probability integral transform) was really good. So good, in fact, that multiple people had had the same idea previously, and at least partly independently of each other. Happily enough, a guru in the field pointed this out to me when I circulated a preprint and didn't savage me, but pointed out shortcomings of the rPIT and possible new lines of inquiry. The paper has just been published.
Bottom line: your simple idea may be good, but chances are that those ideas that are both simple and good have already been worked on.
No, you cannot write a paper out of a simple idea. A simple idea contributes nothing. I guess we all have simple novel ideas every day.
However, if you ground that simple idea within theory, and/or build a theoretical framework, with suitable references to existing literature, and you demonstrate that this hasn't been done before, and maybe explain why it hasn't, and suggest how it might improve on existing alternatives, then that's a paper.
If you take that theoretical grounding and then set out a plan of implementation, together with a monitoring and evaluation framework to assess its impact, together with a comparison against existing alternatives then that's a paper.
And if you implement it and evaluate it as above, then that's a paper.
If you want one higher impact paper rather than three lower-impact papers, and if journal space allows, you could do all three of those things in one paper.
Warning: Harsh answer following.
@energynumbers has covered some of the aspects of why a "simple" idea is not enough for a research paper. It needs prior literature search, must improve on previous methods, a theoretical justification why it should work and an experimentation section providing the benefits of the idea, compared to previous state-of-the-art.
Still, when I read your original question and your later comments, initially I thought you were joking. Without wanting to be harsh, I could not believe that sending bulk SMS to unemployed people is your idea of fighting unemployment or meaningful research. As a computer scientist myself, I try to refrain from suggesting ideas about problems I do not have not the capacity nor the knowledge or the necessary background to understand. And your comments like "even cats and dogs have cell phone" not only show you know nothing about unemployment but you are also indifferent and ignorant to this huge problem's social implications.
But let's stick to the "scientific merits" of your idea. Any EU country has an unemployment rate of (very rough estimates) 4% (Germany, Austria) to more than 20% (Spain, Greece). That means that even in countries with low unemployment rates (e.g. Germany), sending a SMS to unemployed people would require 3,4M SMS. Since, the unemployed should answer these SMS by yes or no that means another 3.4M SMS. Who will pay for those 7M SMS of your idea? Even for a big city (1M people) that would require at least 8K SMS for Germany or 20K SMS for Spain. Perhaps you are implying that the unemployed people should pay the response SMS from their pockets, for their "right" to participate in your "novel" research? You also seem to assume that all unemployed people have internet connections (for filling in their data) and cell phones, when usually unemployment benefits (if they have not expired) can only cover very basic needs. And you also want to force those unemployed people to fill another form for giving you their data (and who authorized you to collect this data? It will be probably illegal in many countries) besides registering to the respective unemployment agency and sending bulk CVs to potential employers for hoping to land their next job. This is not only insensitive but borderline silly.
Bottomline: Research is a very serious job. Not everyone can do it. Especially when there are sensitive groups and people involved. Treat it as such. If your concept of research is ideas that come to you when you are ordering french fries or you are in your bathroom during your "physical" duties, you are WRONG. Otherwise your "research" ideas would sound like the infamous French phrase "Qu'ils mangent de la brioche". They will not only lack any scientific merit but they will also sound insensitive and ignorant.
UPDATE: a) At the OP. You (and I) are no Newton. Even if someone hit you with all the apples of the world, you will most likely develop a head trauma than the theory of gravity b) As others have commented, brilliant ideas can come anytime but ONLY after studying a problem for weeks, months or year. Check the term Eureka effect, why that happens. c) Even after studying a problem for a long time, the majority of the ideas that one comes up with are not necessarily good d) Even if you come up with a brilliant idea, it needs weeks of work on pen / paper, pc or lab for that idea to actually be publishable. e) What "most people grasp" is not scientifically correct. People believed for thousands of years (some people still do) that the earth was flat and the sun revolves around the earth. So, basing your scientific ideas on "common sense" has no scientific merit. f) If you do not believe me or the others commenters, try to publish your "simple" idea and wait until the peer review replies back. Then you will have your answer.