Perhaps I can respond first. When we discussed this matter internally, the issue was never raised; it was not a primary concern. As for our members, I cannot say whether they support the idea of extending eligibility to all Employment Insurance benefits.
From a more practical standpoint, I have trouble understanding how such a program would work. It might be at odds with what really constitutes a self-employed worker, who has a great deal of autonomy and independence in terms of control over his or her work. So I think that I have more questions than answers.