Many people have 6% of their gross income deducted for their 401Ks. That can be stopped at any time, and is a hefty chunk. I’d say in general for the same net income, the person who gets it after saving 6% is a better credit risk than the person who gets it without saving anything, all things being equal. The lender has no way of making this distinction without the stub.
So, why do you want to use a canceled check again?
In addition to the other reasons already given for why gross pay and not net pay, don’t forget those ratios. They’re calibrated for gross pay. There are guidelines for lenders that say things like “maximum debt:income ratio for a borrower with no housing payment is 35%.” That’s gross monthly income to debt payments - actual debt including things like child support but not including things like utility bills. Computers filled with data have determined the risk involved in lending to people with a debt ratio of x%, and each individual lending business is free to determine for themselves what kind of risk they’re willing to assume. Also, let’s not forget that things like disability and unemployment insurance pay out based on a percentage of your gross pay.
Of course no one will give up health insurance to qualify for a loan - they don’t have to, given that the lenders qualify them based on gross pay. They also don’t have to tell their company to stop withholding for taxes, no really, I’ll pay them myself in April, to qualify, because that wouldn’t help either. I can fiddle with my net pay a bit by changing my withholding and my insurance coverage, but my gross pay only changes when my employer changes it (or I change employers).