I like D1 factions, but I also think that faction rallies have the potential to be even better. My main gripe with the "current" faction system is that it never feels like the factions are dueling, but instead, it was just another thing to grind. If you look at the last rally, people only really cared about getting the catalyst they wanted. I have a few ideas to try and fix that.
We can stick with the lost sector system we had before, but with an overhaul. Instead of just going to that one fastest lost sector and grinding public events, we could have each faction trying to control the separate patrol spaces. So each patrol space/planet is treated as it's own entity, meaning that NM and DO could be fighting over Earth by getting as many lost sectors done as possible, while FWC could be gaining a huge lead on Mars. Also, we could overhaul the whole "grinding public events to get a debuff to get a greater amount of tokens" system. I think a better way around that would be to purchase a variety of consumables from the faction vendor that will give you different debuffs, that in turn boost your rewards. This way it makes the rallies competitive between factions, and make doing the event itself more varied and strategic.
Another idea is to add on a crucible game mode where you are matchmade with your faction. it doesn't have to be anything special, but it would add to the flavor of the event, and spice up PvP just a little. I mean just adding any new limited-time events besides Iron Banner to the crucible will make it more fun.
I know that all this would take a ton of work and will likely never happen, but I can still hope that something vaguely similar happens.