As much as the 757 was designed to be a 727 replacement, her introduction really came at a time when the 727 was just into its prime as the short- and medium-haul "weapon of choice" for the US majors, and many others around the world.
I think the 757 ended up replacing the 707 even more so, as at time, aircraft such as the DC-10, L-1011, and to a lesser extent, the Airbus A300/310 were flying routes that the 707 filled well, but the widebodies were operating with a bit too much capacity. In addition, some 707 flights were downgraded to 727 and 737 equipment, clearly too small for some jobs. The 757 fit the bill perfectly, and thus the two types were able to coexist quite well for some time, until the 727 was ready for replacement.
I can remember, in my early days with my company, Eastern, Republic, and Delta were just introducing 757 service, it was hailed as the aircraft of the future, and was referred to as the "perfect 707 replacement" by a pilot I sat next to on an ATL
757 flight in the mid-80s. Those were the end of the golden days, especially when you could go to almost any major airport and see at least a few 707s rolling around!