I don't understand. CIs are equivalent to computing a bunch of p-values, by test-interval duality. Should I interpret your points as critiques of simple analyses that only test a single point null of no effect (and go no further)? (I would agree that is bad.)
Yes, I argue that individual p-values (as they are used almost exclusively in numerous disciplines) are bad, and adding more information on effect size and errors are needed. CIs do that by conveying (1) significance (does not include zero), (2) magnitude of effect (mean of CI), and (3) errors/noise (width of CI). That's significantly better than a single p-value (excuse the pun).
