Stay at home shouldn't be compensated for taking care of their children. Money has to come from somewhere. The man who works at the donut shop earns his money by making and selling donuts. The mechanic makes his money by fixing cars. In these cases there are trading in goods or services for money. Parenting isn't like that. Perhaps they will be compensated by their children taking care of them in their old age.
I find it funny that so many mommie types will give an emphatic yes to this question, then turn right around and blast "welfare queens" for pooting out kids to stay on the dole. I guess it really is different when it's your own, huh, ladies? I don't think any stay at home parent should get compensated for choosing not to work. Sorry, but you can't have it all.
While stay at home parents certainly do a lot of work, no one doubts that, that does not mean they should be compensated. They problem with the assumption is the fact that there is no source of funds to pay them from. If it is a two-parent household, one persons funds are covering all of the expenses.
While two people are together and if one of them is taking care of the children at home, that person should feel entitled to share the income of the partner. It should not be state compensated though. And if there is a split of the couple, then the years of taking care of children should be factored in at a given rate.