You're forgetting about FICA/Social Security which can be as high as 12.4% of AGI for every dollar earned below $150k or thereabouts. A stay-at-home spouse doesn't pay social security but nonetheless benefits from it (and in certain states, can do so tax free) upon retirement or death of the breadwinner. That's not a discount available to an individual taxpayer or a double-income household.

Filing as married allows for higher tax exemptions, in many cases around double the individual tax exemptions. For a high earning breadwinner this is as much as twice the "normal" buffer of untaxed income for investment before incurring a phase-out. If both spouses were high earning there wouldn't be much of a difference between the average exemption per spouse and the exemption provided to an individual taxpayer. Sometimes it's even less than if each spouse had filed seperately.