You're right about the power of the grinder. Most of the girnders I see "for home use" are suitable for ginding bologna for sandwich spread or stew meat size cubes of beef that have no tendons or silver skin. To grind venison, beef for hamburger (as used in the meat industry), or pork trim for sausage it's best to buy a "commercial " type grinder that's at least 1/2h.p. or larger. We use a 1 h.p. Hobart grinder.
Most people will resist the grinder they really need because of the price. It's a catch 22, you need to spend money to save money.
Dave