I worked (mostly) at SAIC in the 1980s and 1990s. In the groups I worked in we developed large software systems (sometimes with hardware components) for customers. Software reuse was a dream back then that was largely unfulfilled. Our procedure for reuse was mostly cut and paste from old projects, with some effort to write reusable libraries. There was also a movement to use commercial off the shelf (COTS) software.
It occurred to me recently that we are now much closer to the dream of widespread software reuse. What has changed is a healthy open source (and libre) software ecosystem of trusted and vetted libraries, frameworks, and complete applications. I tend to trust software from FSF and the Apache Foundation, for example. Organizations and individuals are motivated to release software for a variety of reasons: for help in development and bug detection, for good publicity and self promotion, and sometimes for ego. All good reasons!
My process when starting a new project is to first identify existing open source software that I can build on. My choice of programming language is often dictated by the language used in the open source software projects that would be most beneficial to my project. It is a thrill to build a new project using mostly existing software. This greatly reduces the cost of projects and I think also greatly increases developer satisfaction. Who wants to spend 6 months writing a project mostly from scratch when it can be done much more quickly building on other people's work.
For me the magic that makes this all happen is public repositories like github and bitbucket. The cost of evaluating an open source project for reuse can be very low: a git clone, build, run the tests, look at the tests, and read through the documentation and source code.
So I believe that we have made incredible progress in software reuse in the last 30 years.