We do, and most of that data is focused on errors (eg., already registered, bad credit card, etc), although we do about 30% of events like "quote requested", clicked "sign up", etc).
We ended up creating a "sidecar", that processes the event, checks again our CRM in place (Hubspot, Zoho) and either proactively initiates a conversation via email, or sends transaction confirmation/error. (We store templates for different events, and adjusted to different channel - depending which one we know for the customer - like Push, SMS, email).
Would you use something like that?
If not, why not?