My logic is, I would be paying for a lease so I might has well build up equity in a mortgage instead and if I found a fixer-upper then have equity also.How did you find this deal and how did you negotiate it?

I concur with @John Underwood's logic and agree with @Kevin Lefeuvre that Airbnb's solution works better (at least in my market).

You then use that logic to say that swapping a mortgage for a HELOC in first position is not a valid strategy because the numbers can be replicated by keeping the mortgage.  

Logically, if you fall into any of these fields, get a property manager:Located far from your rentalAren't familiar with the laws in your stateDon't have a way to properly fill work ordersI prefer going with PM's because they alleviate the stress of dealing with the property itself, so that I have more time to focus on other things (like getting more properties!)

You could post a request for those lists, but you won't "Own" them (logic behind them).

The reasoning, as I remember, was some combination of 1031 exchange, increasing ROE, and leverage.Does anyone have a good resource or explanation summarizing the logic?

I would recommend Logical Property Management they are a member here on BP and not only be a good PM but Drew can help you with a lot of knowledge that he has with all the years he has been doing it. 

Otherwise you should be prepared to pay a professional for things you cannot legally or logically do on your own. 

["If the house burns down, we'll just take the insurance payout"...pyromaniac logic LOL...do you overinsure your properties on that hope?

You're right in that it makes no logical sense so my best guess is that it's an emotional thing for them they have to work through.