To clarify, there is no such thing as a "no-PMI" loan. These are "LPMI" / "Lender Paid" PMI loans - mortgages that have a PMI contract with the cost built into the rate. It's tax effective at lower loan amounts, but perhaps not so much given the 750k threshold for deductible interest. I defer this piece to USC to calculate the dollar benefit from a taxation perspective. That kind of knowledge is significantly above my pay grade.
General rates for 20 percent down might be 3.5 (example only) with 85% being 3.625, and 90% being 3.750-3.875. Each higher rate tier is due to the higher cost of that blanket PMI contract. I recall Wells Fargo had an 89.99 LPMI option but haven't heard any updates about that product for some time. Remember that LPMI is a misnomer. Since the rate is higher, it's borrower paid PMI, structured as interest costs.
There are "sign and drive" mortgage loans out there. Unfortunately they aren't at reasonable rates or terms. That's actually a good thing IMHO since publically backed Banks and Credit Unions should not be creating loans with at one time a 75 percent failure rate. Production of these kind of loans were off loaded to private investors where their capital can be risk priced correctly. A Seller Carry Back is an example of a "sign" only type of loan, albeit rare in this day and age. Assuming one of the "mass production providers" of easy qual loans is pricing their mortgages at 6.75 percent a seller might be able to get a 5.75 percent return on the carry back. That's not a bad deal if one is OK with the overall risks involved.
My .02c