You can't address poverty related inequality through healthcare and education. Not entirely sure why people think you can.
You can however address the issues that keep people in poverty, eg disability, poor mental health, substance misuse and caring provision all of which are under the control of the Scottish Government.
If we had decent support for people with disabilities, supported teachers to teach and provided decent social work and social care services instead of expecting schools to be a one stop shop. Our drugs deaths are incredible but even before that addiction services are poorly funded and provision is sketchy. Assessment for children with additional support needs is a fight from start to finish, and then getting good child centred support is nigh on impossible.
Mental health services are dreadful particularly if you need anything other than CBT, there’s little access to good, long term, trauma informed therapeutic support.
All of this sits well within the devolved powers and would help people out of poverty. People wouldn’t need to stop working to care for children with disabilities, or for vulnerable adults, their mental health would improve allowing them to access the job market and sustain employment, the fall out from substance misuse would significantly lessen, children in care would have much better outcomes.
Health and education might not fix all the issues, but they’d go a very long way to addressing inequality. The Scottish government have form for being quite blinkered, not listening to professionals and over engineering/micro managing just about every area of public/private life. They don’t use their existing powers well, why would we want to give them more.