As you mentioned you have 5 screens in a screen flow, work object will save on the last step. Now if the work object is not saved in 2nd and 3rd step, how do you want it to be routed? If it won't be saved, how another user would see the current state of the case?
Screen flow is meant to be completed by a single user - agreed
If you want to perform by different users, you need to split the flow and create different screen flows and assign them accordingly - which user action will take the precedence if a work object will save on the last step