The thinness would make it harder to grip laterally. It's less surface area to grab on to.

That may be the impact for some people, but for others, who can now get another metacarpal around to the other side of the phone, it will be easier.

I do hope that the metal they are using is on the grippier side (like the black 16 Pros, as opposed to the 16s)

I feel like I must be one of these people because even a regular iPhone from the past 5 years is way too thin to comfortably hold. When something is much wider than it is thick, not aligning it perfectly in your hand puts pressure on it diagonally and sends it spiraling to the ground.

I noticed in one of their videos, where the subject is picking up the Air off a table, it looks like it could be hard for a wide-fingered person to pick up.