The downfall is that this method is very time consuming. The chances of you seeing some of these animals is highly unlikely. Time and money constraints add to the challenge. There is a way capture the animals that you dream of. Animal preserves and non-hunting game farms provide that opportunity very nicely. There are many places located throughout the world. They can be researched out beforehand. I find word of mouth to be very helpful. I only seek out places where the animals are well cared for. I also look for opportunities to photograph the animals in natural settings which requires the facility to have large enclosed areas. Obviously, there is a cost for this. The fees that are paid to the facility help cover the costs of feed, staff, maintenance, and other expenses associated with the keeping of wildlife animals.
Workshops provide a great opportunity to capture images that you have dreamed of. A professional photographer (me) is at your side helping you with your camera settings and composition to help insure that you get the photograph. I also provide instruction in Photoshop and Lightroom during our down time so you get the most out of your image processing. I provide all of this at a lower cost than you would pay booking the facility on your own.
If you have not taken a photography workshop, I highly recommend you give it a try. It is a great way to capture images that you have dreamed of, and have the help available to insure that you are proud to later show your images.