"Under federal legislation, gainfully employed mothers are entitled to maternity leave, but there is no law granting fathers the right to paternity leave." [0]
Add to that, the cost of health care and child care:
"half day" day-care system. [1] Subsidised day-care is at 50-150CHF a day! [2]
If you are looking to re-locate to an EU country, you might find better options where work/life balance is greater AND cost of living is lower. [3] However, the pay-scale is probably adjusted to the cost of living.
[0] https://www.ch.ch/en/paternity-leave/ [1] https://www.swissinfo.ch/eng/society/children-and-childcare/... [2] https://www.expat.com/en/guide/europe/switzerland/10476-chil... [3] Estonia, Sweden, Finland, pdf => https://ec.europa.eu/social/BlobServlet?docId=19932&langId=e...