The usual logic goes like this: life insurance replaces income, the stay-at-home parent doesn't earn income, so they don't need coverage. I've heard it from clients for years, and I understand where it comes from. It's also wrong.
Run the actual replacement math. If the parent handling childcare, school runs, meals, and the household calendar died, the surviving spouse doesn't get to keep working the same job the same way for free. Childcare alone runs four figures a month in most of Oregon. Add after-school coverage, summer care, and the sick days a job won't absorb, and the number gets uncomfortable fast. That parent produces enormous economic value. It just never shows up on a W-2.
There's a second cost people miss: the surviving spouse's career. Plenty of widowed parents cut hours, pass on promotions, or step back entirely for a few years. A policy on the stay-at-home parent buys the family the option to grieve without also restructuring the household finances in the same season.
I'll concede the fair point. If the budget only stretches to one policy, cover the earner first. Lost income is still the bigger hole. But term coverage is cheap enough at most ages that covering both parents is rarely an either-or decision. See what term actually costs before assuming it's out of reach.
Something to note: insurers usually cap coverage on a non-earning spouse relative to what's in force on the earner, so the two applications tend to travel together anyway.
How much? Price what the work would cost to replace for however many years the kids need it, then add a margin. A needs analysis walks through exactly this, and it doesn't cost anything to run the numbers.