Because land has an inelastic supply, and therefore its value is driven entirely by demand. Banks already charge as high an interest rate as they can get away with (i.e. one commensurate with the buyer's credit rating and the value of the land); trying to raise it to account for LVT would immediately backfire due to the resulting profit loss (in this case, from people being less willing to take out such mortgages).
The bigger issue is what happens to current mortgages. If I paid 25% down on a 1.5 million property and have paid my mortgage down further so that it's now sitting at $1 million and the value of my land is $1.25 million and the value of my house is $250,000 when the government adopts Georgist policies the value of my land goes to $0 which means my property is now worth $250,000 and I owe $1 million on it. I'm obviously going to walk away from the loan so the debt holder for my mortgage gets an asset worth $250,000 instead of the $1 million of money they were owed, a loss of $750,000. I also lose the $500,000 I had build up in my home since I walked away entirely.
I think that would be true for any reform that's actually effective in driving property values down.
You're comparing a roughly 80% reduction in house prices with a promise that taxation will absorb further rises in the asset price of land to a 30% reduction in house prices with a promise that the market will eventually recover and grow to new heights. The first effect is nearly triple the second one, the change in future conditions makes it even more extreme.
If the bank pays the tax, why wouldn't they pass it on to the mortgage holder in the form of higher interest rates or other fees?
There are exceptions when businesses are investing for growth and expenses are paid by investors, but normally no business is going to agree to a contract where they lose money. The money to pay expenses comes from customers.