The length of a bachelor's degree is often 4 years, a Master's about 2 years, and a PhD 4--forever years. This is pretty consistent across countries and disciplines give or take a year.
My question is: what is the rationale behind how long it takes to complete a degree? When or how was the current recommended length in years developed?
Specifically for a U.S. bachelor's degree, four years is a learning requirement, not a duration requirement. By that I mean that institutions are constrained, by accreditation, tradition, and sometimes by law or regulation, to require learning (work) that can be competed in four years by a student working at "full load." Where I taught, there was a legal requirement that specified the number of credit hours needed for a degree.
Some, perhaps many, students take longer—often much longer—than four years, but they complete the same number of credit-hours as the student who finishes in 3-1/2 years. Some degrees, e.g. architecture, are five-year programs. Similar reasoning applies to masters' programs.
Note that, in the absence of such a learning requirement, a university could just hand out degrees. We call those "diploma mills."
So, the answer with respect to undergraduate education in the U.S. and often elsewhere, is that the amount of learning (work) is established by tradition and often embodied in law or regulation. Someone who can complete that work in fewer than four years is free to do so; someone who takes longer is similarly free to do so.
Doctoral programs are different; the work is set out, at least in general, and can often be completed in about three years, but the student is time-limited to seven or ten years to be sure actual progress is being made.
For some recent history: The Bologna Process started 1999 with the aim to reform and somehow unify the higher education in Europe and has created the European Higher Education Area. During this process many countries reformed their system of higher education and also established new degrees replacing old ones (for example Germany replaced their "Diplom" and "Magister" by Bachelor and Master degrees. The Bologna declaration does indeed state that the "completion of first cycle studies" (nowadays called Bachelor in most participating countries) should last at least three years and also that "The degree awarded after the first cycle shall also be relevant to the European labour market as an appropriate level of qualification."
So far for the history of the length of a Bachelor degree (at least in Germany). As for the rationale behind the three years, I could only guess (but I won't). The Wikipedia pages do give a pretty good starting point to find more information on this topic - for example you can find the ECTS User's Guide which gives a lot of information on how the degrees should be achieved. One thing is that 60 ECTS points should make n academic year (on average) and that each point should correspond to 25 to 30 hours of work… I don't know if any of these things or the respective documents answer your question, but this is basically the de facto answer to "Why 3 years for BSc and 2 years for MSc?" (at least for Europe).
Degrees are standardized by the institutions that give them out, so that they correspond to a certain amount of work; whether that is coursework, teaching, labwork, publications or literature study.
They not only say that you are qualified but also that you have done a certain amount of work. Now, one can (and probably should) take the notion that a certain amount of time invested into something measures your competence with a healthy portion of skepticism. But how else would that be quantified? You could make a case for grading, but that's a whole matter of speculation as well (just one such article, there are many out there).
So, when we assign grades to students, what are we really measuring? Are we measuring effort? Are we measuring the ability to memorize stuff? Are we measuring the ability to explain things eloquently? Are we measuring the ability to anticipate what will be on an exam?
At any point, there are several different programs out there which correspond to different levels of work, for example there are 1-year and 2-year Masters programs, and PhD varies anywhere between 4-6 as you mention it yourself. My PhD was 4.5 years, 1 year of it was supposed to be coursework, half year corresponding to teaching and other dept duties and the rest to be my own research.
Another important aspect is typically funding. I cannot say how it is in the US but in Europe (or at least Scandinavia) the PhD positions are typically tied to specific grants and they are then allocated budgets before the doctoral student even starts. That being the case, when the money runs out, you are expected to be done. :)
