It was so much better than the windows way of running a random program with little visibility, and so sad when so much software changed away from that method.
In practice personally auditing the installation script for every program you're going to use and the installation script for every update is grossly impractical, for the same reason nobody reads EULAs. In the end it still boils down to trust.
Even if you are adding a third-party package repository, you just change the downloader. Although you usually get signature checking with that step for free.
And therein lies the issue: It's not the job of the software developers to provide packages for your distribution, but the job of your distribution maintainers.
So, if your distribution will probably not backport $newver of some tool to your release, you are only left with installing it via different means.
If you find yourself always installing software like this because your package repositories don't contain what you want, it may be a good idea to just check out different distros.
That's a very different scenario from having to download the dependencies as well.
The reason it's a "very linux problem" is exactly because this is a sane thing to do in a pool of insane systems.
There's absolutely no reason to ship your 1k executable with 1Gb of libraries, used by 10 other programs.
Sure something bad can still do things, but it tends not to splat files everywhere with no trace.