Overheads do represent a significant part of institutional income. It makes sense in many ways, but, in essence, it leads to the antiefficiency principle: Since overheads scale with the direct research costs, universities and research institutions, more or less directly, tell their research staff: "do your best, for as much money as possible".
The title of this post is provocative because the quoted statement above is not as antiefficient as it sounds. "Do something for as much money as possible" would be antiefficient, but the actual statement implies two maxmisations, "your best" and "as much money as possible", that is, maximise both input and output.
Here is the tricky thing, the efficiency of the system depends on how much weight we put on either maximisation, which depends on various subtle mechanisms, very much in the research culture of the different countries. A balanced system can be well tuned, in the sense that output quality defines the likelihood of new input (with provision for entering the wheel as starting researcher). In the UK the balance is (at least partly) kept by the fact that, complementing the overheads, universities are also funded by direct evaluation of their output in a national research assessment exercise (now REF). The system/culture also depends on time: in some particular country it may have worked well at some point, but then becoming more antiefficient with time.
The fact is that many institutions evaluate researchers by input, using grant income as the key component of their evaluation. That is certainly an aberration. The thinking is: if the researcher has secured the grant, somebody will have evaluated the researcher, and somebody will evaluate the output of the project. It implies that the institution delegates away the assessment of quality of the output. It has now even become common that the input is perceived as the goal in many processes and evaluations. Capacity for raising funds is the wanted trait, whatever done with the direct funds (once the overheads are secured) becomes a secondary consideration.
Some research institutions in Europe have become specialised in attracting European grants (a sport demanding very specialised skills) while not so skilled for the execution of the corresponding projects. I have witnessed situations in which such a research institution gets the grant and, after securing the overheads, they subcontract the actual research work to a private company. Probably an extreme and quite minoritary situation, but, nevertheless, illustrative.
It is the downside of an otherwise sensible model that has worked well in some places for decades. We researchers just need to be aware and help keeping a healthy balance in our own contribution to evaluations, while reminding institutions about the antiefficiency principle.
I have a naughty proposal in this context. To the many bibliometric indices currently used to evaluate research, we could add the index of citations per dollar. Technically hard to measure (not so hard for large averages, such as per country). As any other index, it would need to be wisely used in conjunction with other metrics, and always allowing for differences among fields of research, etc. It is nevertheless intriguing what the landscape would look like when using it. After all, we owe it to the tax payer.