That would indeed be OK for when we integrate with the agent. In most cases we do, but we should be forced to. An EC2 instance without an agent that is in a running state (and thus not captured as having an issue by your current checks), but has an instance check failure would not be reported as DOWN or TROUBLE. That is basic monitoring, and it should be reported, regardless of using an agent.
System checks on the other hand can't be checked with an agent, it's an AWS level metric that is also vital.
So while the presence of the agent solves things for some cases, for others it doesn't.