PhD without compulsory publications hurting profile
Programs do get reputations. 

And a program that produces good students who don’t have publications, especially if they are a well known school, will still have good placement rates. 

Faculty too can get reputations, positive and negative. 

Post-doc and hiring committees take these reputations into account when evaluating applications. If we know a school or a particular faculty member produces (otherwise stellar) students who don’t have publications, we’ll use other criteria to evaluate them. 

The same thing goes for faculty who are known to write over the top recommendations and those who write acerbic ones. They all get calibrated in the end. 

Where it does hurt you is with industry positions as there, reputations aren’t as well known.