That is only a religious belief. If two programs share a common library, an upgrade to that library (say security fix) could fix things for one program, but introduce a hole into the other. Every upgrade to some shared piece must be validated by the developers and QA of every program that uses it. 99 programs could be fine the change, and the hundredth could break.
And if you want utmost reproducibility, then you in fact need a given version of a program to have its exact dependencies, so that you're running exactly what the developers are running. If program X needs libfoo.1.2, and program Y needs libfoo.1.3, and the programs are actually bundled with their specific version of libfoo, then you have better reproducibility than if libfoo.1.3 is foisted upon program X because program Y requested that version.
The model where you have one libfoo only works if everything is open source and packaged by an upstream distribution, which takes care of curating the entire combination of stuff, so that when program Y needs libfoo.1.3, the entire distro is officially pushed forward to that libfoo version; it becomes the official libfoo for program X also. What you have matches the upstream and so behaviors are likely to be reproducible. If the vendors for different programs are completely independent, then you in fact sometimes need multiple versions of dependencies.