ICH E6(R2) in section 8.2.2 does not differentiate wet ink original or copy. It depends on what your company SOPs define. I know the described historically approach as well. It was connected with arguing about the signature page as an agreement having a kind of contractual meaning - and therefore the wet ink original has been collected. If you collect "only" a copy, you may check with your legal department on the company opinion whether a copy is binding. If you leave the original on site you do not need a "certified copy", as the original is not replaced or destroyed. However, in future also investigational sites will more and more use electronic investigator site files and you shift the challenge of filing, certified copy versus keeping a wet ink original simply to another Party.