There is a distinct difference in a full game run depending on how you start it. If you select the first level rather than hitting the "New Game" button in the bottom left. You will keep all of the found equipment and be able to choose from it in all of the open combat mission. However, if you do choose to use the "New Game" button, any open combat missions will reset the items and even plate carriers that you previously found.
This absolutely changes the possible times that you can get. I.e. the highrise mission and being able to reach the roof in about 45 seconds with ascender (recieved once reaching the roof) vs about 2 minutes without.
it should at least be considered as a possibility though it's more likely that the new game+ category would be more popular.
i mean if its a popular enough category then sure, but as of right now i dont see it having enough interest to warrant adding it in
PSA: On open combat missions there is a mandatory cutscene that you can skip through, (except on crash site that one is unskippable.) These must be part of the run. Any run that skips these to "save time" will be rejected. If a run includes this cutscene but then hits 'last checkpoint' to skip
