For your example, "delete first page from all the selected files" you can use the split/extract pages tool, rule "2-".
Create new documents, but with the first page striped, as needed.
Other rules expressions can be used to remove middle pages.
Even so, a merge like tool, where we can define the pages to delete with rule fill accelerators to enter delete First/Last pages rules, will be much more handy for that operation.
Ok, I will try to add the "Delete Pages" tool and split/extract "strip extracted pages from source file" option into next release.