I think it was chosen as definition of success because it is _easy to measure_.
From the beginning of the Web onwards, you had very little idea of what people actually did on your site, but the fact that they visited was an easily counted line in a plain text log file.
The moment something else was available (e.g. actual clicks on an ad, or conversion rate), that was used.
Even if a site gets micro-paid for each video viewed or article written, they still have an incentive to nudge viewers to keep viewing. If you think about it, even if they have a pure subscription model they will want people "engaged", i.e. addicted.
Yes, the tendency of focus on easy to measure metrics instead of what you actual care about is a whole other discussion of interesting craziness.
But isn't that orthogonal to this discussion? There are better metrics, but they still have the same large scale attention economy, filter bubble, junk food media effects as "engagement" does. "actual clicks on ads" is conversion rate x ad views and ad views is a function of engagement.
I don't see how more accurate measurements would positively affect the way content is written, presented and optimized. If anything wouldn't it just get worse?
From the beginning of the Web onwards, you had very little idea of what people actually did on your site, but the fact that they visited was an easily counted line in a plain text log file.
The moment something else was available (e.g. actual clicks on an ad, or conversion rate), that was used.