Warning: This is a thought exercise only. I'm not trying to make predictions, and I realize that it probably will not happen this way, but lets think through this scenario and discuss some potential outcomes.

Assumptions (please don't argue against these even if you find them improbable):

1. Blockchain protocols require technical level trade offs, and these will naturally evolve to favor the blockchain's primary use case over time. This has essentially happened to Bitcoin where its primary use case has become one of a decentralized store of value. Much to the chargrin of many people, its other use cases have generally been pushed off the blockchain as transaction fees are to high to support them, or the protocol evolves in a particular manner (or fails to evolve to allow for other use cases).
2. Ethereum will be subject to the same evolutionary process. Ethereum's primary use case is that of token management. Issuing tokens to raise capital, represent ownership, incetivize behavior, payout dividends, etc. This use case is significantly large enough that if widely adopted, it would fill the network to capacity and effectively push any other use cases not directly supporting the primary one off the network. The protocol will tend to evolve to support this primary use case over time, and fail to evolve to support other use cases.
3. High levels of scalabiltiy are a pipe dream. Blockchain technology purposely makes the trade off to exchange high throughput and scalable architectures in order to achieve distributed consensus. It will be impossible for one blockchain to scale to a high level without sacrificing all the good stuff about blockchain in the process. Therefore, no one blockchain will be able to host all the activity that will want to run on blockchain based networks.

Results and consequences.

So fast forward a few years. Pretend that the above assumptions are true (again, as a thought exercise). What do you think the landscape look like?

There are obviously dozens of potential use case on the Ethereum network with many well funded projects pursuing a wide variety of these use cases. To see these pushed off to other networks would likely cause a lot of angst and division in the community. We are likely to see a lot of drama and controversy as there will be many winners and losers in this process. Would it result in the same kind of political battles we currently see on the Bitcoin network? Would it be even worse than Bitcoin as there will be more factions, and more groups that are looking to monetize directly on the blockchain so are therefore competing directly with each other for that limited resource.

The Ethereum VM and its compilers have become something of a standard in the smart contract industry. There are a lot of development tools and developer knowledge around technologies. If its not feasible for projects to continue on Ethereum proper, they will likely seek out other compatible networks. Those could be existing networks like Classic, Expanse, or Quorum. They could be in development networks like Rootstock, DFinity or Qtum. They could be brand new branches of Ethereum based blockchains. They could be all of the above.

We are very likely to see many of these blockchains start to specialize around whichever use case becomes the primary one on that chain. Many of the existing branches are already doing this, but none of them have really embraced particular use cases so far, so its difficult to think about how they would evolve differently. Maybe one Ethereum based blockchain has some clever way generate random numbers built right into the protocol and it attracts the majority of gambling and gaming DApps. Maybe another one builds in better support for Oracles and becomes a natural fit for many DApps that utilize those. As the industry matures, nearly every successful blockchain based company will likely have a "I wish there was an op code for XXX" that they feel like would help their business. Or "I wish the network was optimized to make XXX op code cheaper so my use case was more profitable"... we could see a large number of specialized networks that are specifically tuned for particular use cases.

In such a world, projects like Polkadot or Cosmos seem like they would be hugely important. Many projects would likely want to keep their asset tokens on Ethereum proper even if they moved their DApp to a different network. There would need to exist ways to make transactions between all these loosely compatible blockchains.