I actually get where you're coming from.
There are people who don't earn a lot but earn too much for benefits.
In Scotland we have EMA which is Educational Maintenance Allowance for pupils who want to stay at school beyond 4th year (16+, not sure what year that is in England, the year after GCEs I think). They get an allowance every week depending on parental income.
Mine didn't get it but stayed on anyway and I felt that I had to give them the equivalent amount but we were skint! It was really frustrating at the time.
However, my youngest son's GF got it and she now has a degree and has just got 100% in a new qualification she studied for. (They have been with each other since they were 15, now she's 30, and he will be at the end of the year). They own their home and have a great life together.
Both my children are now in professional roles. The privilege they had wasn't money (as we didn't have any really), it was seeing us both go out to work every day - and thinking that is normal. His GF didn't have that, but that little bit of money let her see that she could do better than her parents (she loves them anyway).
Your children will see that too.
The best thing one of my children said to me was "I just want what you two have, this house, your relationship, and us four, even though you're mainly skint" 😅
You're a good role model for your children. A lot of children don't have that.
In saying all this, we don't have this nonsense in Scotland as we don't have this two tier system. All of our schools are the same unless you want to pay for the education they would get anyway at a state school (i.e. dafties)