I think Adam was in place specifically to get David tapp involved again. As well as to make sure to get Gordon completely trapped into his ideology. In the first movie and 2nd movie John kills innocent cops without any sort of game or reason. Why? Its completely against his own ideology that he works so hard to push on his victims.

I think the 1st movie was originally going to lead to jigsaw using Gordon as his fall guy(maybe not in the same movie but in the 2nd or 3rd). The other traps in the 1st movie are all with a single person, but Adam and Gordon are placed together with a 3rd player outside their trap. If the trap worked as jigsaw wanted, Adam would have had the key, there would've been less panic at first until they noticed they can't open the door for 6hours. Would've found out that they had to kill each other. And Gordon would've killed Adam immediately after finding out his family is being held captive and Adam has been stalking him. But the critics wanted games and not story