How important is the option for dynamic linking (vs static linking) in the modern day?

Some languages don't even support linking at all. Interpreted languages often dispatch everything by name without any relocations, which is obviously horrible. And some compiled languages only support translating the whole program (or at least, whole binary - looking at you, Rust!) at once. Do note that "static linking" has shades of meaning: it applies to "link multiple objects into a binary", but often that it excluded from the discussion in favor of just "use a .a instead of a .so".

Dynamic linking supports much faster development cycle than static linking (which is faster than whole-binary-at-once), at the cost of slightly slower runtime (but the location of that slowness can be controlled, if you actually care, and can easily be kept out of hot paths). It is of particularly high value for security updates, but we all known most developers don't care about security so I'm talking about annoyance instead. Some realistic numbers here: dynamic linking might be "rebuild in 0.3 seconds" vs static linking "rebuild in 3 seconds" vs no linking "rebuild in 30 seconds".

Dynamic linking is generally more reliable against long-term system changes. For example, it is impossible to run old statically-linked versions of bash 3.2 anymore on a modern distro (something about an incompatible locale format?), whereas the dynamically linked versions work just fine (assuming the libraries are installed, which is a reasonable assumption). Keep in mind that "just run everything in a container" isn't a solution because somebody has to maintain the distro inside the container.

Unfortunately, a lot of programmers lack basic competence and therefore have trouble setting up dynamic linking. If you really need frobbing, there's nothing wrong with RPATH if you're not setuid or similar (and even if you are, absolute root-owned paths are safe - a reasonable restriction since setuid will require more than just extracting a tarball anyway).

Even if you do use static linking, you should NEVER statically link to libc, and probably not to libstdc++ either. There are just too many things that can go wrong when you given up on the notion of "single source of truth". If you actually read the man pages for the tools you're using this is very easy to do, but a lack of such basic abilities is common among proponents of static linking.

Again, keep in mind that "just run everything in a container" isn't a solution because somebody has to maintain the distro inside the container.

The big question these days should not be "static or dynamic linking" but "dynamic linking with or without semantic interposition?" Apple's broken "two level namespaces" is closely related but also prevents symbol migration, and is really aimed at people who forgot to use -fvisibility=hidden.