I WOH full time. DH is basically a SAHP (he does a few hours a week consultancy work) but has at various times over the years worked full-time or part time. Very much his choice. The way i would express it is that even when DH has not been earning, he has been making a financial contribution, in that when he was earning we had to pay for childcare, which we didn't when he was SAHP.
I would not say that him being at home enables me to earn what i earn, because there have been times when I have been in the same role when he did work and I did my job just as well, and i got my latest promotion at a time when he worked full time (and some of my colleagues are perfectly well able to do the job as a single parent or with partners doing similar jobs). Nevertheless I do see him as a making a financial contribution.
I also think the contribution is not just financial - there are benefits to our family in him being at home. The DC like it, and it has enabled them to participate in things that they might not otherwise have been able to (and get more help with homework), plus it takes the pressure off me a bit with things like household admin. However, when we have had childcare (a nanny), the DC have also been very happy and built real bonds with another adult which is nice as our family live a bit of a distance away (they still keep in touch).
I am not sure I (or DH) would say there is value to wider society in DH being at home though. Economically, if he WOH that would be 3 people earning and paying tax (both of us plus childcarer) rather than one. I also don't think having a SAHP necessarily means a better outcome for DC. I know lots of lovely teens and young adults and I honestly don't think anyone could tell whether they grew up with a SAHM or not. I also know the odd bad egg, some who had SAHPs and some who did not.
I feel comfortable in the choices I (and we) have made and really don't care what labels people choose to use about themselves or about WAHPs or SAHPs generally. If a SAHM wants to call themselves a full time mum, i cant get too excited. It does not make me feel judged or bad about my choices or less of a mum when i am in the office. However, i do try to use the generally preferred expressions as I know others do get offended.
I fundamentally disagree that SAHPs work harder though. Some SAHPs work harder than WOHPs, some WOHPs work harder than SAHPs. When DC were little, i did not see being with them in the evenings or weekends as hard work. I most particularly disagree with the idea that SAHPs do not clock off and WOHPs do. When I am at home, I do as much (generally more) with the DC than DH (always have). I have one friends whose (ex-) DH was a SAHP and how very much clocked off the second she got home and they barely some him at weekends. I am sure if it true on some families, but more fool the SAHP for accepting that.
[I confess that the age of our DC is such that it is no longer true that DH is making a financial contribution as they would not need any childcare anyway, but let's ignore that - he now describes himself as retired!]