I think there are too many factors to simply just make a blanket statement that being a SAHP is a luxury. Most SAHPs I know have made a lot of sacrifices to be at home, live in smaller houses, no foreign holidays or nights out, no new cars etc. I obviously know this is not the case and a lot of families need 2 parents working.
A lot of people bought big houses that required 2 incomes, then when the children come along they still need those 2 incomes. A lot of people could be SAHMs but choose not to downgrade their lifestyle and that's fine, it's their choice but don't then tell a SAHP that it's alright for them they don't need to work whilst bragging about your latest car or holiday.
Some SAHPs chose to be at home as the cost of childcare wipes out one salary completely, even working at a loss and it's just not worth the stress of rushing children here there and everywhere to then go and work at a loss. Or your DH works irregular hours or abroad and isn't home for weeks at a time. Or you have a disabled child and cannot get childcare for them 
Then you have the WOHM parents whose parents are the childcare so they get it for free, I know you cannot legislate for that.
Or they only work term time and have school age DC do don't actually need childcare.
What I'm trying to say is that it's not as simple as saying SAHP with a HRT stop moaning and get out to work, two working parents spend pounds on childcare so they need their CB and you don't.
Yes it needed capped, people on 250K for example don't need £20 a week, but it should be done fairly on household income with an additional tax break on childcare for those requiring it. CB for the poorest families should also be increased.