For instance, if I manage to raise private capital to fund a deal and purchase a successful rental property, how would this actually benefit ME when I have no skin in the game (i.e. money of my own invested)?

Others may have a different opinion, but outside of a seller carry back up to 90% CLTV (still require some skin in the game, unless you go true hard money) 2nd liens on real estate for purchase transactions in the manner you're seeking are very difficult to get a loan against, whether it be a secondary market lender (private equity fund, balance sheet lender, family office, etc), and usually are seeking larger transcations ($1-3MM +) in this space, and are still capped at a max 75-80% CLTV (still wanting skin in the game).# 4 usually requires more explanation as its newer to the market (DM me if interested in discussing these options further), but all 1-4 appear to be potential options for you based on the limited details. 

@Henry HsiehTo provide a different perspective:I am NOT a property manager so I have no skin in this game  But I can tell you, as a GP involved with over 1100 units and $140M AUM, good property management is a big key to successful investment. 

For those starting out, always have some 'skin in the game.' 

Yes, grow a thicker skin.

They are not outright scams and people do some deals but you almost certainly would have been better off saving the money and profits and doing it yourself.They call the up front fee your "skin in the game". 

If you don't already own a home yourself, I always suggest house hacking as this gets some skin in the game, but also allows you to learn hands-on and offset your mortgage payments.

I'm very conservative and want conservative leverage percentages, long-term fixed rate loans, high skin in the game and sponsor that has experienced at least one full real estate cycle and lost little to no investor money.

I think you are on the right track however its going to be necessary for you to have some "skin in the game" sooner rather than later - while it can be appealing and seemingly possible to build a significant real estate portfolio with all of "OPM" the reality is you are probably going to need to have some equity in these properties - 20% or so down from your own funds to keep building. 

Needed to get my skin in the game and found a great opportunity with a wholesale deal and had a good visible gap between our buying price and the value of the home so I interested me to this deal because of the way that me and the team would be able to learn and handle these opportunities in the deal to maximize ROI and asset lifespan of performance.