The signature as such is not required (though it is a typical method of implementation). Approval is. One could state that given a controlled set of rights to one person responsible for approval, the appearance of documents in a thus controlled location is also evidence of approval (would practically only work for the smaller companies). Though agreed, typically you would find some demonstrably authentic approval path, whether wet signature, digital signature or traceable system action.
The footer (or header) is an implementation of a recursive mark on succesive cohesive units supporting several aspects. The cohesive unit is something where a loss of integrity is self-evident. A page torn in half, even without further identifying marks, is clearly suspect for loss of information. If a document has two pages, but you lose the last this is not (always) immediately clear without aiding identifying marks.
This is meant for identification (9001:2015, 7.5.2 a), which supports suitability (9001:2015, 7.5.3.1 a) through control of changes (9001:2015, 7.5.3.2 c). This combined with the associated page of total pages it ensures loss of integrity (9001:2015, 7.5.3.1 b) could be identified.
Digitally though, you could replace this by checksums on the pagecount. In the analogue world pagecounts with 'this is the last page items' in a Table of Contents at the start. Ah the room a standard provides.