Firefight, notably, is one type of mode that isn't a big novelty for most players. I find it fun for spurts and moments pending my mood, but it isn't something I'll constantly pop in my disc and want to play on a day to day basis. I suppose part to blame would be map quality - there's only a select few I really had top fun playing, one being 343i's Unearthed. Many others just shake out not very fun.
As for Invasion, I agree it does combine many aspects. In terms of adding objective, it adds mostly Territories, which truth be told, isn't exactly the most popular skirmish variant. They could have had it as territory01, assault02, and capture the core03. Basically how Breakpoint breaks it down. It was a nice attempt from Bungie to give their fans another gametype that features large amount of players, but even then it seems rather less massive than its initial hype. It also kind of stripped out the core of the big-game based Halo, Big Team Battle, and near neutered it in map quality. Perhaps it was good written on paper, but in hindsight it maybe wasn't the best idea for the last Halo game you made.