Advice on REI entry strategy

[Zoe Mercier]

We have 1 rental property that we bought via traditional mortgage and although we got a good deal, we used savings for the 20% down and closing. Our goal is to acquire several more rentals and since we don't have tons of money laying around to keep doing it that way we are trying to do a few flips to build up some capital to buy more rentals. But the more I listen to and read posts from @Brandon Turner about the BRRR strategy I wonder if we might be working too hard? Or maybe I'm not understanding it right, hence this post asking for feedback.

For example, if we were to buy several distressed properties to rehab and sell the plan is to then use the lump sums of cash we would (hopefully!) make to finance the down payments and closings on rentals with good cash flow.

BUT, why then wouldn't we save ourselves work and buy distressed properties and rehab them, then refinance them to get back what we put into them and then start renting them. The goal here would be to refinance only the amount we put in (enough to pay back any lenders and pay ourselves a small amount) to keep the mortgages low to increase the cash flow amount. This way we are only doing one rehab to begin getting the rental cash flow from a single property rather than doing several flips to make enough to not come out of pocket for the rental. 

Hope my explanation makes sense. Based on that, is there something we are missing about either process that someone could enlighten me to? I was a special ed teacher for 10 years and my classroom motto was "work smarter, not harder" and something about our original strategy just seems to violate my code when I think about BRRR. Thanks for any clarification you can give :)