In almost all instances.

Renting a garden unit, for instance, could generate $1,200/month but must comply with city codes to avoid fines.4.

For example, Clearwater FL (famous beach and Phillies Spring Training) does have a 30 day minimum on rentals, making it essentially impossible to have an investment perform well. 

For instance, targeting multifamily properties (2–4 units) is a great way to grow your portfolio.

It seems like there is no catch, would they let me buy a property this month and a property the next month for instance if I have the 25% down+closing costs and can prove that it rents for a decent amount more than the mortgage?

I'd pass OR get it at a no brainer price which we are actually able too in some instances, even if it's listed.

In my instance, my wife and I are currently on the title and would be the sole members of the new LLC.

For instance we have seen dozens of sand and stain jobs on hardwood at $2/sf that needed to be completely redone. 

I do see many investors incorporating a similar strategy with new construction builds, heavy rehabs, or in instances where the property was bought far below market value (usually a wholesale type transaction).

The only instance where it might be more beneficial to do it this way vs. getting financing right off the bat is if you need to be SUPER competitive with your offers in your market.