I almost tried that too back in the day. The stylist did look at me like I'd asked her to stab me in the liver. I - almost word for word - asked for the same thing you wanted: a looser curl pattern. But I also wanted a "frizz free" look. I thought a perm might do that. She wouldn't do it. Told me it'd ruin my hair.
But I did something just as foolish (an alternative form of the traditional curly perm), and I've talked about it here in the forums: allowed a woman to give me a Jheri curl, but I didn't know that's what she was doing. My hair had been down to my shoulders before the treatment and my curls were up to my ears afterward. Also, it looked like an oil slick. And the activator smell? - oy gevalt - was horrible ... Ah the irony of using an activator spray to activate naturally curly hair that has been artificially curled.
What a disaster