If it is a separate premium then you will face the same challenges you do now - where the self employed choose not to pay for EI coverage. And you cannot make a parental benefit premium mandatory.

I think the direction these advocates are heading - is to just give all parents the right to paid leave and address this through general taxation. 

The challenge we have is that increasingly one level of the workforce, generally those paid by the public or with strong bargaining unions,  have access to all benefits, extended benefits, and pensions, whilst the private sector and self employed are being left behind.

How do we level this playing field? Perhaps the public sector haves - could have a bit less - so the have-nots have a more affordable pathway to more.