Would the money in the bank get the same leveraged returns of homeownership? Assuming no market correction downwards, your money in the CD gets around 5.6% (whatever you cited), but in the house, you get 2:1 leverage on a 50% downpayment. So if housing appreciated at the same 5.6% annually, then you get closer to 12% return on your investment. All though no guarantee on the housing market. So the question is what do you think the housing market will do in the next 5-15 years in LA?
Also, I don't think you considered that if you put the $175K into the house, the appreciation of that money in terms of increased value of the house isn't taxable and when you sell, you (I think) get a one time tax exclusion, but with the same money in a CD the interest you receive is treated as income and taxable by the State and Feds every year as ordinary income.