Any cryptocurrency that succeeds in replacing Bitcoin will use the Bitcoin blockchain. Here's why:
Suppose a new cryptocurrency comes out which is a significant advancement over Bitcoin (something no existing altcoin can claim), call it Bitcoin2. Let's say Bitcoin2 uses a new blockchain. People invested in Bitcoin realize Bitcoin2 is superior and realize they should do something. They fork Bitcoin2 into a new cryptocurrency called Bitcoin3 which is identical to Bitcoin2, except it preserves the original Bitcoin blockchain.
That assumption isn't necessarily possible. The advances might not be able to be incorporated into the Bitcoin block chain for technical and/or vested interests reasons.