No, a will does not need to be signed on every page to be valid. However, signing or initialing every page of the will is a common practice and can be used to show that you intended for every page to be included in the document.
A Florida will must be signed by the testator at the end of the will. However, there is no requirement that the testator sign each page of the will.
Although it not required, nothing forbids additional signatures or initials. Indeed, signing or initialing each page of the will is common practice. This is because signatures can be used as evidence that the testator intended each individual page of the will to be included. This evidence would be brought up if there was a will dispute later and someone claimed that a page had been inserted by a bad actor later. This is one of the reasons that I explicitly state in each will I write the total number of pages in that will. Thus, signing at the bottom of each page is fine and can even be useful, but it is certainly not mandatory.