We perform the first high-sensitivity soft X-ray long-term monitoring with Swift/XRT of three relatively unexplored supergiant fast X-ray transients (SFXTs), IGR J08408-4503, IGR J16328-4726, and IGR J16465-4507, whose hard X-ray duty cycles are the lowest measured among the SFXT sample, and compare their properties with those of the prototypical SFXTs. The behaviour of J08408 and J16328 resembles that of other SFXTs, and it is characterized by a relatively high inactivity duty cycle (IDC) and pronounced dynamic range (DR) in the X-ray luminosity. Like the SFXT prototypes, J08408 shows two distinct populations of flares, the first one associated with the brightest outbursts (L_X_>=10^35-36^erg/s), the second one comprising less bright events with L_X_<=10^35^erg/s. This double-peaked distribution seems to be a ubiquitous feature of the extreme SFXTs. The lower DR of J16328 suggests it is an intermediate SFXT. We find J16465 is characterized by IDC~5% and DR~40, reminiscent of classical supergiant HMXBs. The duty cycles measured with XRT are found to be comparable with those reported previously by BAT and INTEGRAL, when the higher limiting sensitivities of these instruments are taken into account and sufficiently long observational campaigns are available. We prove that no clear correlation exists between the duty cycles of the SFXTs and their orbital periods, which makes it difficult to interpret the SFXT peculiar variability by only using arguments related to the properties of supergiant star winds. Our findings favour the idea that a correct interpretation of the SFXT phenomenology requires a mechanism to strongly reduce the mass accretion rate onto the compact object during most of its orbit around the companion, as proposed in a number of theoretical works.