1. I don't agree with the logic, but the CP income rate in large games is indeed wonky. Resources are shared, but command XP is not.
2. With 2 fuel points and 3 VPs you already have the potential to create five frontline battlefields. This game doesn't fully realize cut-off points but those are also potentials for engagements. Problem is, this has everything to do with map design, not game mode. Many of the existing 3v3 and 4v4 maps are not really designed or balanced with gameplay in mind, to put it bluntly.
3. The Brits aren't so much well designed as they have access to more tools and options without doctrine choice than other Allied factions. They're like an Allied Ostheer that has the option to be a major dick in team games.

But even though the t34/76 is in an awkward place, soviet players are still only going to build T4 for the katyusha. The Soviets already have a strong initiative with their T3. Putting out a tank that is weaker than anything that counters everything in Soviet T3 is still a bad investment. (Also what's the difference between skipping a tier and skipping a side tech, really? Having to retreat an engineer?)
4. Yeah the Forward Retreat Point thing can be kind of annoying, especially when you're the lone Ostheer or Soviet. But at the same time, sometimes it's nice to know your army isn't perpetually about to get bombarded with artillery as they reinforce. Plus, halftracks are neato.
5. I feel like this is leaning into the punch. All this means is players would cheese out doctrinal units as fast as they get the fuel. If there's a problem with KTs coming too quickly the solution isn't to make everything else come out too quickly to match.
6. Everyone has indirect fire, except maybe brits because emplacements make the baby jesus cry, and only OKW lack non-doc suppression. The artillery thing is kind of a mixed bag, but commanders are pretty much a choice between what flavor of artillery or heavy tank you want as it is.
Point is, I don't think any of this would particularly improve 3v3/4v4s, but it does highlight that there may be issue worth addressing with how xp for CPs are handled in team games.