Ultimately it is the customer's site. So long as it is within the contract, meaning you're not doing extra work for no extra pay, the customer has the final say. All we can do in such a circumstance is strongly recommend one way or the other and provide evidence as to why we believe that.
Footers, while helpful, are not necessary by any means for some particular types of websites. To me, the worst thing about removing it on some pages is inconsistency. To me, this matters a lot more than whether or not the footer is there. If a user sees it on one page they might think something went wrong for it not to appear on another page. However if the styles of the pages are vastly different besides the fact that the footer is missing it is not a big deal.
In summary, it's their decision provided you're not doing extra work for no pay.