There are only a handful of cryptocurrencies that are worth owning, mainly because they have their own unique decentralized usefulness. IMO, the vast majority of them are just pump and dump coins and number in the hundreds. It's just like choosing a company to buy stock in, you gotta do the due diligence...what is it's potential and who is behind the business?
Diversification is key and just like in the traditional finance world, I believe it holds true in crypto as well. Spread the risk, for example I hold seven assets at the moment, two of which are non-crypto: Physical Gold, Silver, Ethereum, Lisk, Steem, Waves and of course bitcoin. I believe all of those have unique contributions to the crypto universe and should go up strongly during some sort of financial calamity, especially gold and silver.
I know a lot of people get emotionally tied to their crypto which leads to holders of one coin to bash the holders of another, like BTC and ETH lovers frequently do. I've alway wondered, why not hold both?
So yes, I do believe it makes sense to own more than one cryptocurrency.