One can get place renting for $2k, but can’t get approved for that mortgage amount even with tons of history showing it’s paid

I think the issue there is that there's more risk to mortgage companies than "tons of history showing it's paid". There's a reason they use complicated equations instead of interviews to make decisions related to risk. Questions that don't directly relate to someone being unable to pay mortgage:

1. Will they take action that reduces the property value enough to put them underwater
2. If they choose to walk away for some reason, what percent of our investment do we get back?

And with the rest of the equation, home ownership is higher risk than renting because a tenant isn't responsible for damage and repairs. If, for example, peeling asbestos gets discovered and you have to move out to fix it to the tune of $10,000 or more, will that homeowner be able to afford it? Will they just walk out and start renting somewhere? There's a lot of things not covered by homeowners insurance that can financially devastate a homeowner, and the mortgagee (bank) might notice an income disruption that a renter would not.