I don't think there is any getting away from the fact that the premiums for the EI program are essentially a tax (whether in connection with unemployment with job loss or maternity/parental leave).
In addition to the employee premium there is also a corresponding employer's premium. The employer contribution is either equal to or 1.7 times the employee premium. (I get mixed up between the employer contribution rates for EI and CPP). I think the employee's portion is probably between 1% to 2% of employment earnings but there is an annual max somewhere around $1,000 per year (and so does the maximum weekly benefit).
Only individuals who are employed contribute to the program and are eligible for benefits. So, self-employed people are not entitled to benefits.
I think its safe to say that most employers view it as a tax. If you do the math on the contribution rates versus benefits that would be received for a mother who took the max mat leave for, say, two children, it should be pretty clear that the program is basically a form of income redistribution and the program is a tool for social policy. I believe similar programs might be available from private insurers but I think its safe to say that the premiums would be rediculously high in comparison with the EI premium rates but that's because private insurers would price it like real insurance.
Now, even though I think it is a tax, the program is just part of what "is" Canada and a program that all expectant mothers and fathers (and adoptive parents) can get access to. We certainly took advantage of it when my spouse gave birth to our two kids and, on top of that, her employer "topped-up" her benefits to 95% of her weekly pay for somewhere around 16 weeks of her mat leave.