I did it. On all three of my Micklem bridles.
The reasons I did it were: One mare loved the Micklem bridle until I buckled the chin strap. Then she was not happy since I had to force the bit up 2-3 wrinkles and she did not like that at all. I think it put too much pressure on her poll and she did not like having her lips stretched that far. Since she is an elderly Arabian mare I indulged her, and she is quite happy now with the Micklem bridle on her beautiful head.
The other horses I ride did not seem to be bothered by the chin strap, but when I took it off all the bridles the horses I ride became much happier with me! They are more responsive to my rein aids and their mouths are soft and mobile.
Yes, it looks weird. Since I do not show I really do not care how odd it looks as long as the horses are happy. It may look better if the rings for the chin strap were cut off, but I kept these rings for the far off chance that one day I will need them to keep a horse’s mouth shut (a long flash strap will work, ending up with 2 layers) or if I tried the bitless options again (I have the multi-bridle Micklem.)
I did rip out the stitching instead of cutting the leather off. That way if I ever desire to I can have a saddler sew the straps back on to the rings on the noseband.