A few years ago we built this exact thing for an airline that you have definitely heard of. I believe it ended up being shelved due to internal politics/shuffling, but it encompassed everything that you described except non-travel/lodging scheduling.
The problem with these kinds of systems is that you always end up having to declare one person the de facto dictator/organizer (which effectively mimics reality), and the whole experience is perhaps overkill for groups of less than 6 people who would likely just conduct the informal planning over an SMS group chat.