I agree.
We had a Lurcher bitch who came from a long line of fox dogs, but when it came to the crunch she couldn't handle it....absolutely lost the plot, pee'd herself, ran off, everything.
My husband decided to let her focus on rabbits, which she loves...she's a brilliant rabbiter...she's a day dog....she tackles any cover and gives 100% all the time. He says she's the best rabbiting dog he's ever had.
She's Bedlington/Whippet/Grey. Her Dam was Bedlington/Strong Whippet and her Sire was Bedlington/Grey first cross. Thirteen years old now and still going strong.