One can readily "get by" without having a chain plier. There are work-arounds.

One can barely "get by" without a chain breaker.

Now, if you're willing to have a bike shop do all maintenance for you, then you don't need either. But if you intend on maintaining your own bike, changing or cleaning worn chains, shortening new ones to fit and the like, you need both. The last thing is a small piece of heavy gauge wire twisted into a "C", or sold like this:


^ super convenient to relieve chain tension when your shortening or re-joining chains.