I don't think I agree. You don't need root and you don't need to "install" anything with these other options; it allows the user to extract and run rather than extract, elevate, install, run. It clearly shifts some of the pain from the user back to the developer. It's particularly clearly a win if you're distributing your app on your website instead of via distro package managers.

A shell script provided by the app author can automate setting LD_LIBRARY_PATH and running the binary. It's very convenient for the end user. Lots of programs are shipped to Linux this way.

They are easier for the end user in certain cases. Putting the library in the system library search path requires elevated privileges (usually). Having your application run from a self-contained directory does not.