Catherine - you have a portable skill and can get work either f/t or supply I presume. Wait til you start paying child care costs, and then comment.
You will, unless you are lucky enough to have family doing your child care, have to pay. You will be paying per month prep school fees for nursery. You will have to pay that in the holidays as well, even though you are there to keep the place open. Child minders costs as well. When I was teaching and dh was away/abroad, I put ds into prep school to get the child care I needed to do my job and to cover the early mornings to when I finished some planning / after school activities and got to ds at about 1900.
Many SAHMs don't have family around to do their child care; the cost of the child care is more than they can earn, and if like me, their partners are away lots of the time or work abroad, then he can't be there to sit the kids whilst they do an evening shift. Depending upon where you live in the UK, there aren't the part time jobs about, and the travel costs to get there outweigh the wages. Not everybody lives in a city with good public transport.
No one is being 'paid' for being a full time parent; if they were the salaries would make them higher rate. The cb is a token nod to the cost of raising a child from the state. In the cases of higher rate families, then it is more than covered by the amount of tax already paid.
You also need to realise that some people are SAHMs because they have to be - their kids are disabled, or they are carers, or unable to work themselves because they are disabled. One size doesn't fit all as you should very well know from being a teacher. You should also have realised that having one parent at home can be advantageous for kids. Bringing up your kids and providing a stable constant presence for them is not a luxury; it is what most Mums would want to do in the first years of their children's lives, and if they can do that, why not?