Optimally there would be only one blockchain for each PoW algorithm and there pretty much isn't any reason to use your own blockchain if you are just going to use an algorithm that is already in use, since you can always host your own chain on top of it and increase the security on both of them by doing so.
I think the pertinent existing concept is
merged mining. A special form thereof,
blind merged mining, is part of the
Drivechain proposal for sidechains.
Most ICOs are horrible and useless and by most I mean practically all if not all. My advice is always to stick with Bitcoin as there is nothing else that really contributes anything useful.
Quoted, because
you can say that again!
OP, the problem you sketch is part of why some of the better altcoins chose to start with their own POW algorithm, not (then yet) used by any other coin. For example, Zcash uses Equihash; so Bitcoin miners with SHA-256 ASICs can’t suddenly redirect their hashrate to attack and overwhelm Zcash. Given the breathtaking size of SHA-256 hashpower currently in existence, this is quite important. Any altcoin which uses a SHA-256-based POW is incredibly foolish, and not only for reasons of a potential “51% attack”; see what happened with miners gaming BCH’s DAA before their November hardfork. (Though in that case, the vulnerability was by design; in essence, it was a
de facto premine for Jihan & Co. I focus here on the technical issues and possibilities.)
To subject line, on multiple levels: Yes, there can be only one Bitcoin!