I can't say I count "teh campaign" among the main issues of the game, both because it essentially has one (in the form of a series of sequential scenarios loosely connected by a metaplot) and because I always considered "campaigns" in this genre little more than extended tutorial and the "big scenarios" are what I play for.
The original AOW campaigns were great. I also loved some of the carrier-over mechanics. Not just bringing over heroes, but bringing over veteran units and resources, as well as race relations being retained over scenarios. Being able to choose your campaign branch was great as well.
AOW2 and AOWSM weren't as good, but still good.
Don't forget that some campaigns have great and memorable scenarios which don't work outside of campaigns. United Cities, Hall of Heroes, Valley of Wonders, Death 1...
I think the way to go with campaigns is treat them as a campaign of Challenge Scenarios, after the first easy campaigns.
Honestly I would have loved an AOW-style non-linear campaign with a structure closer to that of the original game, mixed with the one done in the RTSes Earth 2150 and Warzone 2100:
- Multiple branching missions like in 2150 and in the original AOW
- Not just win-case but also lose-case. Lost a mission? You can still continue the campaign, but your enemies get buffed in subsequent scenarios. You might even have some loss-only scenarios.
- Goal not mission-oriented meta-campaign (like how in Earth 2150 you need to get enough resources)
- Missions with carry-over map which retain what you built up before
imagine starting a campaign, building up in the first scenario, going on an expedition to a different scenario for mission 2 (bringing over heroes, and being able to choose units and resources to bring over, akin to AOW), then coming back to mission 3 an expanded version of the first map which carries what you did in the first, and also expands the "Mission 1 map" out, revealing new lands in a bigger map. Let's call them "Home" and "Away" missions.
It would really make the 4X-esque elements pop out, if you could go back to what you built up previously.