> If I want to run the software, it's better to download it in a format my CPU can understand, rather than download source, figure out the dependencies, wait for compiling (let's say it's a large project like Firefox or Chromium that takes hours to compile), and so on.

If its a choice between downloading a binary that depends on a stable ABI and compiling the source. They way most Linux software gets installed is downloading a binary that has been compiled for your OS version (from repos), and the next most common way of installing is compiling source through a system that figures out the dependencies for you (source based distros and repos).