If 51% attacks begin emerging, the chain still functions. People just need to require more confirmations. Then you require so many confirmations that the 51% attacks aren't profitable any more.

This kind of chain might become very slow, but still have the same properties as blockchains do have.

Btw the same thing can be thought has having a block time of 1 min, where de facto standard is awaiting 10 confirmations, versus just having 10 minute blocks.