Which countries cover high childcare /elderly care costs?
Most European countries, actually.
They also provide a genuine safety net against unemployment/incapacity for all citizens, by giving state support based on your previous contributions - not means tested - for a limited period.
So unlike in the UK where after paying tens of thousands of tax every year for decades, if you lose your job for 6 months you can end up losing your home ... other European countries recognise that helping you with the cost of the life you have for a few short months means you're likely to actually get back on your feet. You actually get a meaningful safety net out of all that welfare you're paying into.
Likewise, most give a state pension which is based on your average income (hence contribution), over your working life, usually up to a maximim which is about twice what you get if you contributed nothing at all during your whole working life. To support pensioners continuing the life they are used to - and because it's fair.
All this is possible - and in fact the norm in the rest of Europe, which people for some reason believe is more socialist than us 
Incidentally, that link between previous contributions and welfare in other EU countries but not the UK is arguably what made free movement a problem for the UK and led to Brexit.