Personally I'd say the best idea would be to add an option when creating a co-op game which allows you to select how the combat situation works - ie set to to a timer for moves for those who are concerned about this issue, and allow it to be set to no timer for those who are not concerned about this issue. Just need to make sure that anyone joining the game knows exactly which way this option is set, so they can decide if they really want to join or not.
I feel this is the best option, as it satisfies both groups without forcing one group's playstyle on the other. Both groups can play the game the way they want, without feeling like they are being forced into something they do not like.
However, as has been pointed out - even if no option is added, if there is a demand for it then likely there will be mod(s) created to allow/force this kind of thing - assuming the game engine actually allows for it. You just need to look at most other games which allow modding - people have created mods to adjust gameplay to satisfy how they want to play (harder gameplay, more detailed gameplay, etc).
