I probably take 20 - 30 deer/year. If it is cool, I let them hang a few days or if I have access to a cooler, I let them hang. Most of the time in this part of Texas, it is warm and I at least muscle them out and freeze, then process further at a later date. The only thing I soak is cutlets, prior to frying. I have soaked them in buttermilk, milk, milk and egg, jalapeño juice, beer, and Miracle Dip just to name a few. I did not do this to remove any flavor or blood. It makes me feel good and makes the flour mix adhere to the meat better.
I process my own so I that all contaminates have been washed off. They do make a product that you can spray on the carcass that kills or slows, the growth of bacteria. I also shoot mine in the neck or heart/lung shots. I have not gut shot a deer in years, and do not mess the shoulders up either.
I realize that I am very lucky in being able to hunt in my back yard, and if not, real close to a cooler or residence. If I were hunting away and took a deer, and it was hot, I would skin and quarter it. Then I would place that in a cooler with the drain open and keep covering the meat with ice. My main purpose in this would be to cool the meat while in transit.
Sorry to ramble, but I am a no-soaker, and I have never had anyone say that my venison had a gamey or deer taste.
PS: I have given away, or thrown away some deer that had been eating excessive amounts of Cedar. They stunk, the meat stunk and I got rid of it. No amount of soaking was going to cure that smell.