For what its worth, many package managers support some method of exporting a list of installed packages to a file (or in a way that can be easily piped to a file), and its not difficult to pipe a file of packages into a shell loop to get the behavior as described.

Native support in the package manager would be nice, sure, but the Unix philosophy of providing tools that can easily augment each other to solve problems means this is generally a trivial thing to implement by anyone in a way that works best for their use case.

Also Zen exists, which is a Firefox fork that implements the concept of Arc