I agree with you that modern web projects tend to suffer from build dependency creep - but I don't think Composer alone really counts as being heavyweight or unnecessarily complex, even for a small project. It's just a phar archive and a json file. That's not really the same class of insanity as, say, requiring the Node.js runtime and npm to import a build system to compile the CSS assets for a PHP project.
Even if structuring a project around the PSR autoloader adds a bit more complexity (probably little more than adding a namespace and moving everything into a folder) that's still preferable to the dark days when everyone just rolled their own autoloaders (if you were lucky) or you were expected to do it yourself (and then maybe everything gets wrecked because of a relative path somewhere in the mass of includes of includes.)
Even if structuring a project around the PSR autoloader adds a bit more complexity (probably little more than adding a namespace and moving everything into a folder) that's still preferable to the dark days when everyone just rolled their own autoloaders (if you were lucky) or you were expected to do it yourself (and then maybe everything gets wrecked because of a relative path somewhere in the mass of includes of includes.)