I just retired after a 28 year career in mortgage technology.

Here is my take:

First, modern mortgage origination is a scale business based upon quantitative processes that depend upon collecting data of very poor quality to measure the past, present and future prospects of the borrower in order to answer a simple question :

"What is the willingness and ability of the borrower to repay the money we loan them?"

(This quote is taken directly from the Fannie Mae automated underwriting manual.)

The Past is measured by their Credit Score, i.e. how they have behaved when money has been loaned to them in the past.

The Present is measured by the appraised value, down payment size, Loan-to-Value ratios and other deal oriented metrics, including potential appreciation in a given Metropolitan statistical Area (MSA). i.e how much skin does the borrower have in the game?

The Future is measured by the Housing-to-income ratio and various
assets-after-closing metrics and custom rating scorecards. i.e. do they earn enough to make the monthly PITI payments? How stable is that income?

For your example, 2-3 years after a mortgage is funded, for a given borrower, almost all of the data used in the original underwriting decision will have changed. Jobs changed, divorces, economic downturns, bad investments, different interest rates, and on and on. The lender will definitely have changed their underwriting standards.

Just because you qualify for a mortgage today, definitely does NOT mean you qualify automatically again in 2-3 years, even if rates are lower.

Secondly, lenders today almost always immediately sell your funded mortgage either directly to the GSEs (Fannie, Freddie, Ginnie, etc.) or to Wall Street as part of a large pool of similar mortgages called a Collateralized Mortgage Obiligation. ("CMO").

A CMO is actually a corporation, into which the lender has quit claimed many, many mortgages. The corporation issues a bond, the interest on which will be paid by the interest payments of all the mortgages in the corporation. CMOs are typically over-funded to account for mortgage default risk, so a CMO that issues a $50M 3% bond will actually hold about $52M of 3% mortgages.

For the most part, mortgages in the United States can be pre-paid at any time, like if you move or win the lottery.

This however, creates a problem for the bondholder of the CMO your mortgage is in. They were counting on your 3% interest to pay its part of the interest on the $50M bond for 30 years, but your mortgage is now gone. Its payment stream has to be replaced.

The owner of the CMO acts as trustee of the corporation and has the authority to replace your pre-paid mortgage with one of "like quality" and payment streams.

This great when interest rates are rising because they can replace a pre-paid 3% mortgage with a recently funded mortgage of 6%. This is awful when interest rates are falling because they have to replace your pre-paid 6% mortgage with multiple 3% mortgages.

This creates a reverse incentive to NOT help you refi when interest rates are falling, IF THEY ARE STILL ACTING AS THE TRUSTEES OF YOUR CMO. However, if they sold off your CMO, they WILL help you to refi, but because someone else owns your original mortgage, they have to treat you as a brand new customer, and as such, charge you all the usual fees for origination, so again, no auto-refi is possible.

The best solution of what you are looking for is in the Danish mortgage market.

If interest rates rise, the street price of a bond with a lower interest rate drops. Why would I buy a $50M 3% CMO originally issued two years ago when I can buy a $50M 6% CMO bond issued last week? To reflect the difference in income streams, the price of the 3% bond drops, so you can buy the $50M par value 3% CMO for only $41M. The yield to maturity on both bonds will be the same.

This is where the Danes got really clever.

In Denmark, in addition to pre-paying your mortgage when interest rates fall and you refi, you also have the right to 'buy' your mortgage out of the CMO bond when interest rates rise and the street price of the bond falls. The price you pay is whatever percentage your mortgage is of the total par value of the bond.

So if you have a $500K mortgage that is in a $50M par value 3% bond and the street price of the bond drops to $41M, you can "buy' your individual mortgage out of the pool for ($500k/$50M) $41M = $410K

This is a pretty sweet deal for the consumer, which unfortunately has zero hope of adoption in the US.