There is a downside to multi-compartment pill containers: it's not practical to determine what is in each compartment.
For example, when you go into hospital (in the UK, at least), you are expected to take your medicine with you. This helps the doctors and pharmacists get an accurate drug history - especially if you're not compliant with what your doctor has prescribed.
If all your pills are in a multi-compartment box, they can't be reliably identified, their quality can't be assured, and they have to be discarded - even if your prescription hasn't changed.
(It also assumes that you know which day of the week it is, and can figure out the time of day - probably not much of an issue for the slashdot crowd, but for those with aging parents, it's something to bear in mind)