How typical is it for a team member to pitch an entirely new feature or system mid-development and then have it ship with the game?
It really depends on the scope of the feature, when during development it is pitched, and who's actually going to build it.
Obviously, scope on any feature is important. If the feature or system will require dozens of developers or hiring a bunch of new people to build, it's a really big ask and the leadership will have to weigh it against the current scope planned for the game. If scope grows too large, something has to give - we need to cut something in order to make it all fit within our development schedule. As such, any approval must consider the cost, both in resources and time, and whether we have room in the budget and schedule for it. If we really want the new feature or system, then we're probably going to have to cut something else to make room.
Because building a feature or system takes resources and time, the time at which the feature is pitched is important. If there's insufficient time to build, tune, and test the feature/system before the game ships, there's no way it can get a green light logistically. When I first had these sort of ideas mid or late production, my more experienced coworkers would tell me to remember those improvements and file them away for the next game (which later became "save it for a future update"). I return to those ideas now and then, because it's also a really good learning experience to build something and realize that there are better ways you can do it. This is also the answer to the classic interview question about "if you could go back and do something again, what would you change?".
A given pitch also holds a lot more weight if the pitcher is also the builder - I've seen a lot of "wouldn't it be cool if...?" ideas thrown around over the years from a lot of people, but the vast majority of feature or system pitches I've gotten green lighted are the ones that I built myself precisely because the people I was pitching to knew I could do it. I still remember one time when I pitched a feature idea to my boss and his first (and only) response was "Can you build it in two weeks? If so, sure." Blue sky dreams and ideas are fun, but we're always looking to make things real. The ability to back up the idea with action is a really strong argument in favor of any feature or system.
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