I think people are overcomplicating it.  An attacker only needs one longest chain to attack.  Sure you could run a multithreaded application and try simultaneous attempts to build the best longest chain but that's about it.

But I don't think peers operate this way.  All chains except the best/longest are discarded.

If I'm an attacker, I wait until I have a long enough chain and then I broadcast it.
If peers think that is the best one, they will use it.  And if they don't, they won't.
Either way, nothing increases exponentially for me.

The blockchain never becomes a block tree because that is moving in the opposite direction from consensus.
Everything quickly converges onto one chain when you have a proper mechanism in place like best chain wins.

Generally no, because you'd only be competing against yourself.  If you are an attacker, you want to put maximum resources on building one best chain.

If you're talking about separate attacks (doing a double spend and then later, doing another one) that's another story.

Its like this, you can always get a single individual/group to set up up multiple pools in PoW/PoS, or multiple delegates in DPoS and grab more share than what it seems. But the hard cap means that it is more complex to get the same control.

Say, Ghash sets up another couple of pools anonymously (or maybe even does), or makes buddies with a couple of other big pools, then it already has control. In DPoS on the other hand, he/she/they have to go through a lot more trouble (some 50 delegates in case of BTSX) to get the same control.

Besides, say, a pool offers incentives, then everybody will naturally flock to it. Sure, at some they might start getting worried and not go, but as we have seen in the Ghash case, appealing to the better sense of the mining equipment owners doesn't work to well. They might not even be too worried about the long term health as they might be just looking at it as a business. In DPoS, the hard cap means such a scenario is not possible, and you have to also keep in mind that the users of the coin are the ones who are voting.

I agree that excluding transactions could be bad in a 51% attack against bitcoin.
I would like to see more proposals like using sidechains or something to increase
The work an attacker would have to do to maintain a malicious mining monopoly.

how could that be a problem. proof of work can be considered a proof of stake system in that you are proving your stake in the collective hashing power of the network. The value comes from the stake not from the cost of proving that you have stake. Thus,  the reduced cost of pos mining is not a problem but a solution.

I think I see which direction you are coming from. But I do not clearly see how a hard-cap is going to solve the problem of a second pool under control of the very same real-world entity.

"A lot more trouble" Why? Are existing pools preferred before new ones?

Lol.  Yep, I agree.

Not a problem for Bitcoin, certainly.