A dynamically linked library need only have one image of itself in memory.

If you are running a process that, for example, forks 128 of itself, do you want every library it uses to have a separate copy of that library in memory?

That's probably the biggest benefit. But it also speeds up load time if your executable doesn't have to load a huge memory image when it starts up, but can link to an already in-memory image of its library(s).

The only real downside is exporting your executable into another environment where the various dynamic library versions might cause a problem. For that we have Docker these days. Just ship the entire package.