Geico/Progressive do not offer them - they offer homeowner's insurance, condo insurance, renter's insurance and etc, but none of them covers the building structure & the common areas. 

On paper what you're describing might sound doable - but it sounds like your perspective on REI is based off of knowledge of only the "good parts" Managing and owning rentals (yes, even with a PM & price point of sub $50k) comes with its own challenges and headaches. 

All applicants are screened the same based on credit score, criminal history, landlord references, etc.

It's all about supply and demand for your specific offering. 

Based on both of your posts I’ve done a little math and calculated I would have to charge $255 a night (at a 44% occupancy rate) to stand the smallest chance of making what would make this worth it to me.

The house is situated in a desirable neighborhood but it seems they are only looking into cash offers. 1.

I would encourage you to offer a "move in special" to your tenant. 

It's allowed me to do some of my own work like changing toilets and fixing leaking ceilings, but even if I don't want to do a job personally hopefully I'll have enough knowledge to not let a contractor over charge me, or recommend something I don't need.You'll also meet local contractors, and hopefully investors.They may offer an employee discount too.

I placed an offer, which was accepted that day. 

You would want to offer less and then negotiate concessions after the inspection.