The idea and process is basically sound, if rather hurried. The problem is that the evaluation is really fiscal in nature - does this project pay for itself or not - and doesn't take other factors fully into account. This really should be the first step in a two-step process: First evaluate the direct fiscal value of projects. Then evaluate the larger political/societal consequences too.
The fiscal value of military defence, for instance, is probably dubious for many countries. It's a very expensive system preventing very rare threats. It may simply not be cost-effective to prevent a once-per-century invasion. A small police force-like coast guard and a professional rescue corps could do most or all that an army does in peace-time at a fraction of the cost, while a bit of the savings could be used to pay off would-be invaders, or rent an army short-term from a friendly country when needed. Ridiculous? Of course. There's value in a national defence force beyond the direct fiscal balance in the perceived safety and stability.
We could keep just the few projects with direct societal impact and quick pay-off and stop funding basic research, long-term projects or anything highly risky. That is absolutely an option, and if you're in financial crisis and you have to choose, science is certainly not as important as, say, functioning emergency services or health care. And no matter how well off, no society can afford to finance research in everyarea. You need to choose. But to choose wisely you need to know the consequences of your choice.
So, what are the consequences of not doing research in a particular field? We'd not lose the knowledge - the research would mostly still be done somewhere - but lose the ability to use it.
A modern country - that "information society" thing - lives and dies by the skill of its people. That skill is more often than not imparted through higher education. Educators at that level are normally required to have a research degree - a doctorate - and are often also required to do some amount of research along with their teaching. Why is that? It's because doing research is the only way to become intimately familiar with a field, familiar enough that you understand where the field is going, and can decide what to teach, not just how. So you need people with research experience to teach at your universities and colleges. Medical doctors need research experience too, and company labs need young researchers to staff them.
But that means you have to offer ways for students to become researchers. You can't become a scientist just by studying - you need to actually work in real research projects. And the current teachers are also researchers, remember, and need to do research along with their teaching. Not to mention that they're researchers because they find it fun and rewarding. Scientists as a group are very mobile - a couple of colleagues of mine have worked in six countries this past ten years - and if you remove their ability to do research, including "useless" but interesting projects, many will simply pull up their tent pegs and leave.
So you do need enough research funding to support the research activities of university faculty and graduate students, or you're going to find ourself without good quality higher education in the field. Which will soon mean you'll find yourself without many of your brighter young people as they leave for better training abroad, and frequently not coming back.
"OK", you say, "so fund applied science, things we can use. Skip the abstract stuff." But applied and basic research isn't really separable. Applied research feeds on the advances in fundamental science, and theoretical science is often guided by the needs of applied scientists. Many research projects employ people from both ends of the spectrum and researchers themselves sometimes drift back and forth over time.
Look at mathematics, which at the research level may seem hopelessly abstract and useless. But it's long been tightly coupled to physics and has evolved as a tool in response to the needs of physicists. More recently the information sciences have also influenced the development of mathematics, and benefit from it in turn.
So if you want graduates skilled in a particular field you do need to support both applied and basic research, and enough of it to sustain a community of researchers. And it will mean supporting high-risk as well as low-risk projects and enduring a fair number of disappointments and outright failures. Research projects do in other words have a value beyond the immediate cost-benefit calculations, and projects that support other research in turn even more so.