Going by what Lapis states in this clip:

I have a theory that the reason the homeworld gems thought that the war was lost to them is because the CG killed a diamond in battle, more specifically, Pink Diamond.

This would lend credence as to why there are only 3 diamonds left, why Yellow Diamond hates Earth, and fusions. I believe that PD was killed by a fusion of the CG, possibly this one:

Source

Fusions of different gems is already terrible enough in the eyes of the homeworld, but killing a diamond with one, that was the tipping point. It's a possible reason as to the creation of The Cluster.

Just a theory I've had since first watching that clip.

Perhaps, they wanted revenge so YD wanted to kill Earth with fusions...

5249945 It would explain why the homeworld gems fled in such a hurry, seeing a diamond die in battle is a horrifying sight for them.

As Lapis said "It soon became clear that there was no hope in stopping the rebellion, all the homeworld gems fled".

This leads me to believe that every option the HG had was considered and used, even having a diamond appear in battle, which I imagine is quite rare.

5249955 My only question is, why do you think PD is the one???

5249958 Because her symbol was removed from the Diamond Authority logo, likely after the rebellion.

Old logo:

New logo:

But what if the pink diamond logo was taken off because rose is pink diamond, or a close associate perhaps. What if PD was actually the leader of the rebellion?
5249961

5249939 Interesting. But it's never been specified that there are only 3 Diamonds. So far, we only know of Yellow and Blue; Pink and White were indicated by the symbols on the Gem moon base. But losing a major Gem in a fight with a fusion would explain YD's hatred for the planet, considering BD was ready to shatter Ruby for accidentally fusing with Sapphire, so for a Diamond to lose to one, it would piss off YD.

5249964

because rose is pink diamond

She's not Pink Diamond,

or a close associate perhaps. What if PD was actually the leader of the rebellion?

Then where is she now?

5249971 It'd explain why she created the cluster, to destroy the planet the CG fought so hard to protect with the very thing they used to protect it, fusion.

5249982 Bet she never expected that plan to fail so miserably.

5249984 She likely never expected anyone to find it in the first place.

5249989 From the wiki.

Yellow Diamond

One of the Diamond leaders. She is the superior of Jasper, and many other Gems "made" for her. She is the former superior of Peridot, now a Crystal Gem. She commenced the Cluster project when Earth was deemed unfit for a colony, due to the Rebellion.

What I wonder is, if she started it after the rebellion succeeded, how did she manage to get it in the Earth? Apparently, force fusions were post-rebellion...

There's a missing link somewhere.

5250000 Probably the same way the CG are still finding hidden structures in the show, they just stopped looking and started settling down to live on Earth.

5249961 If the larger triangle is anything to go by, I'd say the remaining three have potentially given a higher authority to a Green diamond as a result.

A separate theory of mine goes as follows:
Going by both Garnet's origin story and how Peridot explained that that Yellow Diamond controls the military power, and how she herself was a technician, we know that Yellow Diamond is in charge of military movements. In Gem culture, this being preparing colonies by exterminating life and setting up Kindergartens, and we can assume is then followed by Blue Diamond who runs the Gem aristocracy and plans the layouts of other structures, such as communication hubs and warps, which is likely followed by White Diamond who is probably in charge of hard labour gems that actually build and maintain the things.
This leaves the question of, "What was Pink Diamond in charge of?"
The only things I can come up with is either ensuring the proper formation of gems(which, tying into your theory, could explain why Amethyst was left in the ground too long), or research and development in the various Gem sciences and technologies.

5249939

While I think it's obvious that Rose is Pink Diamond, I think the killing the diamond part is true. My theory is that the Crystal Gems all fused together killed White Diamond. My proof is the gem found in the Pyramid Temple. It has the same cut as Yellow Diamond and Blue Diamond. And the column it was trapped in ha a similarity to the picture of white diamond in the mural.

I think that the Crystal Gems kept White Diamond's gem as a trophy and built the Pyramid Temple as a memorial to all the gems lost in the battle, but then Rose used the gem to power all the twist and turns in the temple, just in case the Homeworld Gems tried to retrieve their leader without telling the other gems.