Well, not necessarily. I think the main 2 chains with zero fees are Steem and EOS. Steem earlier allowed for unlimited transaction even if your account had negligible Steem staked. But now the amount of actions you can take on the blockchain are directly proportional to the Steem staked. So you would really need a lot of Steem staked in your account for say a transaction DDOS attack. And that's quiet risky. I mean why would you buy a large amount of a token just to bring down its own chain. It would be like burning your money. Of course rival chains may find it useful, but then crypto users are so vigilant these days that stunts like these often backfire.
Same for EOS. And EOS takes a step further by actually banning accounts with ill intents. But yes, thing with these types of chain are that they are very centralized which itself is a negative point.
That makes sense. Otherwise, if negative activity on a blockchain wouldn't be punished, then the attacker could get away with disrupting the entire network. At least, EOS has Block Producers which have the power to freeze accounts (although heavily centralized). While Steem also has a mechanism to help protect against transaction spamming (as you've said earlier), it's up to debate whenever DAG cryptocurrencies like IOTA or NANO would do the same. The security of such cryptocurrencies isn’t proven unlike PoW, PoS and DPoS. Which means that if zero-fee transactions on a DAG don't get punished, cryptocurrencies using such model will be doomed to failure.
After all, there's a reason why Satoshi implemented a network fee within Bitcoin. If he/she wanted Bitcoin to be fee-less, then he/she would've done so within the early days of launch. However, Satoshi had a purpose for Bitcoin's fees, which makes it highly expensive to attack the network nowadays with a flood of transactions.
Nonetheless, if zero-fee blockchains become highly secure and viral, they could be the future of crypto as we know it. Just my thoughts