If EA would ever read this thread, they could no longer hide behind their bullshit reason of "the fans just don't know what they want".
Anyways, onto what makes a C&C game for me.
I got started into C&C with Tiberian Sun. The amazing cut-scenes/story-line, immersive environment, easy-to-get-into game-play and decently challenging campaign really captured my full interest and I wanted more. From there on, I went and bought RA1 and TD and afterwards every C&C that came out afterwards. What makes TS/FS stand out from the pack was its captivating environment, the rich tiberium diversity just made it feel like the whole map was alive and the soundtrack just made it all come together. That's exactly one of the very few flaws I want to point out in TW: the rich diversity in tiberium wildlife really adds to the amazing atmosphere (FS was the best at this).
Now, onto the general C&C formula. To me, what really made the C&C games stand out from the pack is the in-depth Single Player experience. Aside from Generals & ZH, no C&C game was truly competitive MP-focused and shouldn't try to be. I'm talking a variety of different types of missions, like commando missions or missions with pre-deployed units to vary up the majority of the missions (which involve base building).
Which brings us to base building. The build order of PP, barracks, refinery, etc. is legendary C&C material. The structure of the build order and tier structure is simple, but proven to be very popular. Don't change the core; the only thing you could play with is possibly adding a higher tier (like in KW with the epic units, for example). But let's not forget how different strategies can be very effective: both turtling up heavily or aggressive unit-based strategies are both viable in the game.
Tank rushes. C&C is notorious for its tanks to be amazingly effective for rushing. Add in a super-heavy (anti-everything) tank in the mix and you have another C&C ingredient. Of course, it's possible to slightly diverge from this (like C&C3 and RA3 did) by making anti-tank infantry very powerful, but never make the mistake of eliminating the tank rush.
Keep it simple. No 5 different unit abilities, nobody wants excessive micro-management except the very top of competitive RTS players. C&C3 was amazing at this, providing a little micro-management - this way you don't lose track of what C&C is known for - macro-management.
No capture point X shenanigans in C&C please, thank you very much. If you want a capture RTS, go play CoH or something. Another reason why C&C4 failed as hard as it did.
Relatively soft counters. RA3 was especially guilty of ignoring this principle. In general, if you spam enough of one unit, you can overwhelm the opponent - no matter what - in C&C. It's part of its charm; there's no need to balance the game endlessly for competitive players. Rifle soldiers are capable of killing tanks and enough rocket troopers can kill a rifle soldier. No need to change this.
Other things to consider:
Alternative Singe-Player content was amazing both in ZH and RA3 uprising: commander's challenge and general's challenge. Provides time-extensive additional SP content and significantly increases replayability (that's not the skirmish mode).
Adding Generals and Subfactions was one of the additions that I really loved in ZH and KW. Really spices up the game, even though it's not necessarily core C&C content.