I agree with your basic idea accept for the credit score. Credit scores only show haw good you are at using credit cards. Banks need to start looking at peoples budgets. My credit score is low, but it is because the only debt I have had in the last 3 years is a mortgage. I don’t even have a credit card.
Within two years, I expect to have 6 months worth of bills in my emergency fund, with the ability to tap my nascent 401K for a loan if the need arises.
Fortunately, I'm a TX resident with about 30% equity in my home.
Mortgage lenders need to do their due diligence and make a credit decision based on common sense and sound financial data...one size doesn't fit all.
Credit scores do take “installment” loans (car, mortgage, etc) into consideration, but what’s most heavily weighted is having credit cards, paying them on time and keeping the balance-to-limit ratio as low as possible (under 10% is ideal).
The budget matters, but do you pay those on time, that’s more important, really.
Verification of rent should be more focused on too, if you pay rent on time, you’re more likely to pay a mortgage on time.