Thanks, scylla. Getting my PR and then sponsoring my parents is i) a a long away as you mention and ii) not possible since our lives are now in the US and we won't be moving to Canada.
Let me explain our motivation a bit. My parents currently live in India. They are living by themselves and are getting old. We were trying to see if we can wrap up in India and move to North America to either stay with us or close to my in-laws who reside in Toronto.
Since neither of me not wife are US citizens, we cannot sponsor them for a US Green Card. As a result, their stay with us in the US cannot exceed 180 calendar days. We were hoping that they could stay closer (in Canada) while they have to be outside the US. By non-PR, I was hoping there might exist some other means which allows longer stay than mandated by a TRV, and/or get some health benefits, which they will be in need in the future. Since my wife has lived/worked for 20+ years in Canada before moving to the US, I was wondering if there existed any opportunities that we might have missed.