Government policy (which is all of our business) in relation to taxation, benefits etc drives people's decisions to be a SAHP. So it's not just what individual people think. Unless your OH earns well enough to be unaffected by any of that.
Personally I think children do benefit from having a significant amount of parental time in the early years, but unless there's illness/disability this shouldn't be required once kids are back in school.
If 'support' means going 'rah rah do what you want' I certainly can't, in good faith cheer on any friends of mine who decided to give up work without pointing out what she'd be losing. Quite a few of my friends had never considered the loss of pension etc.
And I wouldn't support any policies, as I have seen suggested on here to give sole earner families (single parents excepted) tax breaks because it's a luxury - not a necessity.
I would and do however support better quality childcare/wraparound care, flexible working. And more subtle things like at a corporate level stamping out expectations for people to dedicate significant amount of personal time to meaningless socialising in order to get ahead.
I'm glad that societal expectations are changing such that women are expected to work AND equally men are expected to do their bit. It makes me happy every time I see school drop off/pick ups, plays etc boldly displayed in everyone's calendars. Male, female, junior, senior.
Of course maybe I'm privileged in that I work in a shortage occupation but this is the ideal - of both parents having work and kids. Instead of 'dividing it up'.