What would happen if we had a new rule that all parts of a claim were seen as limiting, not just the “body” and the “preamble” sometimes?

I’m not sure I understand or appreciate the complete scope of the question being asked here.

Generally speaking, all the parts of a claim are limiting, including the preamble in many cases. Do you have specific limitations in mind?

For instance, if you want “statements of intended use” to be “limiting”, then what would happen is that people would try to protect uses of prior art compositions/articles using those statements (just as they do now). Same answer with respect to functional limitations appended to prior art compositions. How these limitations interact with the statutes (e.g., has possession of the function/use been shown in a manner that would satisfy 112; does the recited function raise 101 issues) would not change too much.

The so-called printed matter doctrine would be nullified and replaced with a standard eligibility analysis.

Bottom line is that the underlying policy drivers behind current judge-made doctrines that say “ignore this limitation” would push the statutes into doing the work they were intended to do.