I have worked with public domain material quite a bit. Currently, anything published in the United States prior to 1923 is in the public domain in the United States [1][2]. Some works published after 1923 are also in the public domain if they meet certain conditions (e.g. a work published in 1925 with a copyright notice where the copyright was never renewed), but it can be an extreme headache to work out which post-1923 works are in copyright and which are not.
Although I am in no way a fan of the current system, it at least has the advantage of clarity for pre-1923 works.
In a proposed system of copyright extension, renewal or terms that are in other ways modifiable on a per-work basis, establishing whether or not works are still in copyright would become an absolute nightmare. Consider that, in the US, copyright applies to any eligible creative work at the moment it is "created and fixed in a tangible form" [3]. In the internet age, millions or billions or works are created each day that are protected by copyright. Most of these works do not have a title and will never be registered anywhere, but copyright applies none the less. A central registry of copyrighted works is impossible, much less a registry that records the specific extensions or renewal term on a per-work basis.
In my opinion, the only possible system that can work is one based on fixed lengths of time. If copyright is extendable, the large majority of works will fall into a legal grey area where it is unclear whether or not the copyright has been extended and almost impossible to find out. Under such a system, the only safe approach to handling copyrighted works would be to assume each work had had its copyright extended to the maximum term possible under law, unless it was provable that was not the case (which, as I have argued, would be extremely difficult).
Under a fixed-term system, it is simple to work out whether or not most works are still copyrighted, even in cases where the title, author of record or copyright holder are not identifiable.
[1] There may be some obscure exceptions to this rule, but it holds broadly enough that I have never encountered any in practice.