Measuring community engagement makes sense when your primary mission / core goal is to build a strong community. When I was building a large online third-party Discord community for a university during COVID, I was very glad that Discord exposed a lot of metrics for admins/mods to track. It's obviously important to not "game" the metrics by falling into short-term gain traps like over-pinging users, or encouraging high-volume but low-quality participation, etc. But as long as you are laser-focused on "providing real value" to members, then long-term or multi-cyclical trends of community engagement is a useful benchmark.

But it doesn't make sense to focus on these metrics if your mission is to create a great product -- focusing on community engagement should be just one small aspect of your overall marketing strategy, which should be a relatively constrained part of your overall budget (both in labor and money). And even within marketing, there are many other important metrics besides community engagement.

Soylent had great community engagement but not enough focus on scientifically-guided product engineering. Tons of businesses that get this wrong.

Generally I interpret overcommitment to community engagement as a signal that the founders are overly narcissistic and usually apply a discount the expected future value/evolution of their product.