At least in the SF market what matters is a financing contingency, not all cash vs mortgage. As long as you go through underwriting first and get full approval

At least in the SF market what matters is a financing contingency, not all cash vs mortgage. As long as you go through underwriting first and get full approval (not pre-approval) an offer with a mortgage and no financing contingency is 99% as good as an all-cash offer. Sellers are not impressed by cash offers anymore unless they're the high bidder... in which case it is the high offer not the cash nature that matters. And lenders that work in SF understand how this works and indeed can go through full underwriting without a property having been selected. Appraisal is the only thing that might matter which is why it is a good idea to hold back some cash.