Suppose there are (for example) ten independent blockchains that all achieve consensus using the same physical compute tech (CPU/GPU, a specific ASIC, whichever).
Suppose one of those becomes dominant - say getting 91% of compute resources, while the others get about 1% each.

Then anyone having about 1.2% of compute power on the dominant chain could shift their resources to a minor chain and have 51% of all compute.
Which would allow them to cheat, unless that chain is somehow immune to 51% attacks.

But whether or not anyone DOES cheat, users of the lesser chains would know that the potential exists to cheat on that chain.
Which would make users less willing to use the lesser chains.
Similar reasoning would apply if the most heavily processed chain had less than 91%, just to a lesser degree.

The only way I can see around this is for all of the lesser chains to immediately post hashes of accepted blocks into the dominant chain to enable historical block checking.
But that essentially makes them just sub-chains of the dominant blockchain, not independent chains, no matter how different their protocols may otherwise be.
They can't be used safely without relying on the existance of the dominant chain.

Is this correct?  Does it affect any of the ICOs out there?  I know a lot are based off Ethereum - but maybe some are vulnerable?