On reflection, I think it may be associated with the fact that tape saturation is the mystery element. Any machine capable of both 15 and 30ips will saturate more readily, or at a lower level at 15 ips than 30. Saturation produces a specific kind of compression in the signal which is interpreted as thickening or fattening it, both broadly desirable in certain types of music. This I think, explains the occasional use of the tape deck in mastering, i.e., a digital signal is put through the analog tape record/replay cycle for this effect. In a similar vein, while in the analog domain, sometimes the signal is sent through a tube buffer or another device which emulates one.
