Can one insure a rental at an affordable price? 

How much value do you see in this versus just having great insurance + umbrella policy?

For example an optimized $750K Palm Springs/Indio STR might generate $125-150K in gross annual revenue but after the double digit occupancy taxes, property taxes, insurance and utilities, the actual ROI could be similar to a similarly valued home on the coast generating $75-80K.

Closing “with a real estate attorney” is a necessity for almost all real estate transactions - it does not insure that the participants acted either legally or acted in compliance with contracts.  

Be sure you have your tenants buy renters insurance.  

If you don't have it already, make sure you have a solid rental property insurance policy in place. 

Deposits from the tenant.Security deposits from the tenant in residential dwelling units shall be deposited in a trust account with a licensed and federally insured depository institution lawfully doing business in this State or the landlord may, at his option, furnish a bond from an insurance company licensed to do business in North Carolina.

Are you going to be able to qualify for a loan on a new one with current rates given your W2 job and cash flow.Both mountain and beach are great options and both perform well (insurance isnt that bad when you cash flow a lot of STRs), however have their own complications, particularly if you're going to manage remotely from the triad.Personally, it sounds like you're doing well in your investing career and making good money.

As to funds - what's the worst that can happen that won't be covered by insurance?

That they don't carry the proper insurance and that a parade of people that you don't know annoy your neighbors and damage your property.