Almost all of these things are in the jurisdiction of the member states themselves, and the EU has little power to control them.
If the EU didn't exist, Germany would still be staffing its nursing homes with cheap(er) foreign labour, just done under a visa rather than EU freedom of movement.
If the EU didn't exist, companies would still produce high-quality products for rich markets, and low-quality products for poor markets. (If you want a fascinating example of this, read this Twitter thread about the manufacture of sanitary pads in Africa - https://twitter.com/aprzhu/status/1083278476310913024)
If the EU, ceased to exist, would eastern European supermarkets no longer be filled with "shit", or would local producers continue to export their good produce where they can get the most money for it?
There is a tendency to avoid criticism of the EU and congratulate it for things it does not do, but it is also a mistake to assign all the ills of Europe to it, when blame for them is much more accurately laid on national governments.
Or worse: the care would be become too expensive and peoples arses wouldn't be wiped at all..