The details need to be addressed, and all perinent information should be analyzed before hunting with cast bullets. Here's what you want to determine:
What game species do you intend to hunt?. What pressure is safe for your selected bullet weight? How many FPS is the bullet traveling at? At what point does the lead bullet become a mass of molten lead in near liquid state charging out the end of the barrel upon firing? ( EX: you would not want shoot pure lead bullets at 3,000 FPS out of a 7mm mag for instance, though you could hunt with cast bullets of the right lead/ zinc consistency out of a 30-30 at 1000 FPS.) Do a bit of research on the caliber you intend to shoot, the velocities, and the powder load before hunting with your selected load.
Cast bullets are popular for reloaders, mainly because they are cheap. Tire weights are an example that are popular materials for relaoding, as they are made with a combination of lead and zinc that is suitable for shooting, and they are often cheap/ even free if the right source is available.
You can use a gas check with cast bullets that will assist in maximizing velocities and reaching higher velocities than cast bullets alone. I have shot cast bullets before, and recently aquired materials and equipment to produce some. When using spent brass, a proper powder load, a new primer, and cast bullets- the cost of shooting goes down. If a large number of bullets are made in a batch at one time, then the idea of hunting with them eventually arises.
Handguns shoot at lower velocities than rifles, and cast bullets are more commonly and safely utilized. Often lower powder charges are utilized here.
I'm not an expert though, but efficient.