While I have a few flashlights, I'm spoiled and did not want to get caught without a functioning headlamp. People who never used them have no idea how handy and useful they really are.
In case you haven't already, please let this opinion be known in this thread:
I've carried flashlights for decades, everywhere I go, and wouldn't be without one. Recently I fell into this site, and increased my flashlight consumption by a hundred percent or so. Wandering thru the site, the Headlamp area manifested itself. I browsed a bit, while trying to find a reason to...
www.candlepowerforums.com
I've been using both a flashlight and a headlamp for almost equally as long. My first "decent" headlamp was a quad-AA Fenix HP10, with an outrageous 225 Lumen. Supports diffuser and colour filters. Of course it wasn't actually that good of a light, but I immediately saw the usability of a headlamp.
As to your question regarding the mount, the 2 rubber straps holds the light firmly(!) in place. Almost excessively so, as I often find myself unscrewing the light (on lights where the head can be separated from the battery carrier) instead of wiggling the light body out of the straps.
But if a secure fit is important to you, stay clear of the ones with a metal clamp. I borrowed one such light from a friend to test, and the light got bumped out of the clamp almost all the time during use.
I do not have any personal experience with Petzl or Black Diamond, but I have looked at several models from either brand, and to me Petzl enjoyed a proprietary battery solution too much, and Black Diamond seemed overpriced for the Lumen output they offered.
I know a decision has been made here, but for ease of use, regardless of price, I can recommend the Acebeam H15. The rotary switch is so simple to use, even with gloves. For a more budget-conscious option, I would suggest the Nitecore HC30 / HC33. No personal experience with Zebralight, but I see that name mentioned here so many times, it seems I need to get one...
EDIT:
Regarding the "USB-C charging" part, my guess is the light has a built-in USB-C charge port that you can hook a phone charger to, to charge the cell inside.
Random stolen image: