Lefty, very nice hat! If you remove the side pinches it definitely gives a Western hat more of a rounded barrel look from the front. It can help on a hat with a bit of taper to it. I don't have any side pinches in this hat for that very reason.
Certain Western hats just look better without side pinches. I think it's a combination of the crown height & the crease that effects the barrel look. Think about it; you never see a telescope crease with side pinches or a very tall crown. A really tall crown really magnifies the barrel look. I don't have any side pinches with this horseshoe crease & really like the barrel look from the front.
Try it. They shouldn't be hard for you to put back in if you don't like the look.
HJ, what are the dimensions on the black hat. I really like it and I have an NOS Bailey 50X I've had for some time that I've been trying to figure out what to do with. It has a self felted band that has to go, 5 1/2 OC and a 4" brim. The hat has been on the shelf for a year and I guess I ought to do something with it.