Where your reasoning falls apart is in the fact that there is a certain amount of inevitable turnover in the housing market. Job loss, illness, death in the family, divorce, etc. There are many reasons why a family may have to move and sell their house.
If they are upside down they lose everything.
A long enough period of this feeds on itself, depressing home prices for years and leading to ruin for many well-intentioned families.
3% down is ridiculous.
As a real estate investor, I have taken advantage of the dips to buy properties and can now withstand and even profit from the crashes that always follow this kind of program, but I will confess I am a fat cat getting fatter.
For example, let's say a family is currently making $75,000 a year, or $60,000 a year after taxes. They've saved up $55k and are looking to buy a home that's around $250k. They will buy about $5k worth of housing items after closing on the house.
Option 1: They put 20% down ($50k), combined with the $5k home furnishings have no savings and their monthly payment is around $1,350/mo all in assuming 4.375% 30 yr fixed, $3500 property tax and $750/yr in insurance. A big recession hits, home values drop 20% and main breadwinner losers their job so their income is $25k/yr, they have no equity and they can't afford the monthly payments.
Option 2: They put 3% down, and with PMI, their payments are about $300/month higher. Same recession hits. They are upside down and still are cash flowing negative, but they have $42,500 left, which would by itself cover around 2 years of mortgage payments, while the main breadwinner looks for a job.
I completely agree on average a low downpayment loan is more risky but there are scenarios where it makes sense.
FWIW - the scenario I gave isn’t exactly like my scenario 10 years ago but pretty close, although our income was even higher and neither my wife nor I lost our jobs (and we had ~800 fico scores then and now). Today I own 6 houses/townhomes, including my primary.