When you try it with 6 let us know your impressions for sure.
From what I've gathered, the first thought is that the game overall is just more engaging, simply because there are more characters and points of input involved. It won't make any of the other issues go away, say inventory or party movement or the smaller pool of companions, but it makes them feel somewhat less pronounced as a point of irritation. The perception of the play pace within combat is faster because there are more points where the player is actually in control of what happens. Outside of combat, it makes things like inventory and gear management more engaging since more can be made use of. Same with the story beats and interjections. A larger party means more stuff happens, and ups the sense of scale, makes it more epic.
You're telling me they're trying to compose an epic here, but not using Hexameter?