No, because the principle would be dead. You'd forever have to be an investor, hopping from coin to coin. No reliability as a store of value. That's why it won't happen. Altcoins (meaning alt-ledgers, not alt-protocols) are a fundamentally self-defeating idea, except in catastrophic backup scenarios and as testnets. The window to market an altcoin to a new audience unfamiliar with Bitcoin - so that it wouldn't be an altcoin from those new people's perspective - has mostly closed, making it truly self-defeating as a long-term investment proposition.

Now alt-protocols are different, as they can be pasted on to Bitcoin's ledger via the spinoff method; maintaining Bitcoin's ledger just like a sidechain would try to. If Litecoin, for example, turns out to be better and there's somehow no way to incorporate its better ideas into the Bitcoin protocol, LTC will not be what rises; instead a spinoff of Litecoin will administer Bitcoin's ledger and BTC will rise because it has successfully improved itself!