The only downside is space.  

The question I have is, are there downsides of purchasing a property with traditional lending and then do a cash out re-finance after the rehab is done?

You can consider creative financing options to pay the equity such a Hard Money loan, (assuming the difference between the purchase price and the assumable loan value is a low balance)You can also ask the seller to reduce the sales price (which might be counter productive for seller if they can capitalize on the edge they have given todays high rates)You might be able to use seller financing for the difference in the purchase price and the assumable loan value (downside is that the seller might need the equity to pursue other investments) as mentions by @Christian Ehlers  You can also consider partnering with another Investor looking for the same kind of deal. 

Hello, After diving into modular home builds I see very little downside other than potential timeline sliding longer than anyone wants. 

My follow-up question: from a loan partner's point of view, his position is risky, since his upside is capped by the buyout agreement, but shares the same downside as an equity partner if, for example, the other partner is unable to execute the buyout agreement when the time comes.

We've also added a ton of folks to our investor mailing list, thanks to BP.Frankly, I can't see any downside to giving it a shot and seeing what happens, particularly at just $9/mo (or $90/year)!

The downside is that you may not be able to readily sell the properties. 

There is a small downside to consider, small down payments eat into your cash flow some. 

or I certainly have enough equity in my 13 properties to leverage and move a lot faster but the down side is yes the tenant makes the payment but that is also lost revenue in the form of interest payments on these loans.  

These are precisely some of my thoughts on downside/risk of this investment space.