I am not afraid of applique, I just hate hand work. I doesn't bring me the feeling of peace that it seemed to give my mother when she did it. Now, half square triangles are sorta OK but quarter squares give me the "willies" just thinking about it. I will try curves with drunkard's path when I gear up this winter since I bought that die for my GO cutter. I have made a quilt in the round, a Hopi Sun Quilt. Probably never again. Whew! Just cutting that out was a monster requiring three long rulers to cut each piece and so much WASTE! Love paper piecing but it goes too slow for my charity quilting needs.
All this is to say, I don't think we really have phobias, just comfort zones. And we all ought to step out of them once in a while but that doesn't mean we can't still mostly do what gives us the most pleasure.