They do work. You can draw a straight line from “Engagement metrics” to a working business model that generates real revenue. There are several B2C products that derive their value from engagement. And it is frequently a leading indicator of how viable a product can be.
But like all metrics, one should not over optimize on any one metric - be it engagement, revenue, growth rate etc.
The biggest issue has been a lack of balance between engagement and usability which unfortunately has been dominated by engagement over usability.
I think engagement comes into play in both scenarios (having and not having a business model) and is really detrimental in the latter case.
But if you have a business model then looking at engagement metrics can be incredibly useful in informing a lot of product decisions and shouldn't be disregarded. Just a mistake IMO to optimize for it alone in the absence of other things.
"engagement" only comes into play when you don't have a business model to begin with (and instead hope to carry on raising more VC money or sell to a bigger sucker) so that's the "best" you can do because your actual ARPU is negative.