Why not just wear iPants?
I carry my iPhone with me everywhere I go without a case. That's because I'm wearing home-made iPants.
I put the iPhone in the left front pocket of my pants, then took the pants off with the iPhone still in the pocket. I made sure that the iPhone was at the bottom and along the straight side, which is nearest the inseam. I marked the pocket in two places; one near the bottom of the iPhone, and the other about one third of the way down from the top. Then I removed the iPhone and (without turning the pocket inside out) stitched the pocket together in both places, using the same technique as sewing on buttons, but of course without the buttons. It doesn't require a sewing machine, it only takes a minute, and it won't pucker in the laundry. It doesn't even matter what color the thread is, because it never shows.
If you don't know how to sew on a button, Moms and military guys probably know how.
Now I can slip my iPhone into my left front pants pocket. It stays vertical over the front of my thigh, where it is barely noticeable if at all, but very accessible.