I have a primary residence that may be a cash out refinance candidate. 

What is your Refinance plan?  

Bets of luck to you!

What are you trying to accomplish with the refinance?

I have the option of purchasing a property for cash and then refinancing it, or just obtaining a new mortgage. Assuming no meaningful upgrades are made to the property (i.e., this is not BRRRR), is there an advantage ...

I bought 2 foreclosures super cheap, renovated, rented them, and then when I attempted to refinance, I was told by multiple banks that for at least a year (2 years in one case) the property would only appraise for what I paid for it.

The cons are that you have used your cash, and that sometimes when you want to refinance to pull your cash out, sometimes for a year or more the property will only appraise for what you paid for it.

Unless Amazon moves into the RE market, and starts stacking shipping containers, renting them to millenials as studio apts, and undercutting me on price, I'm going to be good. 3) On the other hand, if liquidity dries up nationwide, as it did in 2007-9, I suppose the worst case scenario is that my bank doesn't want to refinance a few of my 5/20 year/am term loans.

I have a condo that I own outright. It needs rehabbed. The demo has been done. When we hired our contractor, we had the money for the rehab. However, the contractor delayed starting work & eventually disappeared. ...

You have to start your savings regimen all over again (because you won't be able to refinance in the foreseeable future to get your deposit back)!