If the deal can afford accumulating interest, we may structure it that way.

History shows this simple strategy works all of the time and drives wealth accumulation.

A lot of real estate owners do whatever and later they have to do so many things at once.Of course it is good enough to have one fixed asset and accumulated depreciation but it is always better to separately keep track of asset to monitor and analyze later.

Are any of the expenses accumulated while fixing up the house tax-deductible? 

It's not uncommon in hot growing area where houses taking a long time to build for a builder and when the new home buyer put a new construction under contract, once the house is built, the market has appreciated a lot and you sold the house right after certificate of completion and enjoy all the appreciation accumulated during the construction period.Another story for you but on the losing side: before 2008, the market is hot.

They do accumulate trash, old tires on the property.  

Prices are so high how does a person accumulate a portfolio?

If you're putting money into a savings account it isn't "idle" it is being accumulated for a short term expenditure - your down payment.All of these "crowdfunded" real estate deals like Fundrise will eventually go bust, just like all these sorts of investments do over time.

I  bought my first property in 1988, was never easy, but through the years I managed to accumulate a few,  but I shudder to think how rough I'd have it if I was starting out now.

If you purchased 7 homes, have very little of your original capital invested, and have a lot of accumulated equity, it's working regardless of low monthly cash flow...and you can keeping buying property after property with the same original capital.