There's always tradeoffs. If you require people sort at home, more recyclables end up in the trash and/or people missort anyway.
I agree we should incentivize use of more recyclable materials (in place of non-recyclable or more expensive to recycle materials) in general.
However it's still not enough.
I'll elaborate more on that last point. Restaurants should be encouraged to create takeout packaging that is more easily recycled and/or composted. Similarly wrappers, boxes, cups and packets should have a per unit tax for non-environmentally friendly units.There should also be a push towards the use of glass and metal and paper over plastics. Sturdy glass bottles can be cleaned, thermal blast smoothed and re-used or broken down and recycled completely. Similarly metal lids and cans can also attain a new life with ease.