So the house sells for $500k. The buyer needs $25k for a down payment. The seller then says I will sell it to you for $530k, give you the $30k needed as your down payment. The seller gets the $500k they wanted and the buyer gets the $30k they need and only gets a loan for $500k which works out the same for them.

No, i doesn't work as you described. You buy at $530k and you owe $530k to the bank. The seller give you $30k. Assuming that you use that $30k to pay down you loan. Now you own $500k.

That doesn't bring your loan down to $470k like it would if you had put $30k down. The $30k is not free money. It was your money to begin with because you borrowed it from the bank.