Why could this not be run as an actual service. Zillow fronts say 75% of the estimated purchase price, then sells it and takes a cut of the premium, the rest going to the original seller. It's an estate agent with financing.
Because very often the reason you're selling a house is that you're buying a house, and so you need 100% of the value of the sale to go towards your new deposit. It's no good having 75% of the cash now, you need it all as a deposit and the mortgage company isn't going to take the risk that that 25% turns up eventually.
This is a brilliant idea, and if I ever sold my house I would want to do it this way.
Unfortunately most homeowners are debt-leveraged out the wazoo as a result of the artificially low interest rates we've had for the past decade. Once you filter out people who aren't looking to move the remaining cohort is homedebtors. Although something like 1/3rd of homeowners own their house outright those tend not to be the ones looking to move or flip.