Hi Hans,
This is going to be a theoretical answer rather than an empirical one because I’ve not played very many different low whistles. But here goes…
For a given OD and hole diameter covering the hole will be the same no matter how thick the wall is. You finger interacts with the outer surface. For a given ID a thick wall instrument will have a larger OD of course, and covering a larger OD can be harder to do if you have small hands compared to the hole spacing.
Hole sizes and/or position will differ as wall thickness changes A tone hole vents the bore to the atmosphere. The hole is a chimney to the pressure waves in the bore and a longer chimney presents more resistance to the air moving through it if we can think of it that way. Thus to produce the same note with everything else being equal, it will require a larger hole in a thick wall. So while not strictly required, thick wall instruments would tend to have larger holes.
For example, in .113 in material the L1 hole is calculated to be 0.375 in in diameter and placed 11.702 from the bottom end of the whistle. Keeping everything else the same but making the wall thicker to .213 in, the same hole would need to be .418 in in diameter. I used flutomat to do this calculation, which is available here if you would like to explore it yourself.
http://www.cwo.com/~ph_kosel/flutomat.html
If the holes have very square or sharp corners they will act smaller than holes that are properly chamfered or undercut, so in practice there are things the maker can do to make this better.
In addition to reaching the holes there is the response of the instrument. Response meaning how quickly the note responds when you vent a hole. Thicker walls can take longer than thinner because the chimney is longer. But again other factors such as bore diameter and chamfering will affect this.
I personally feel that the material or rather it’s propensity to absorb sound of certain frequencies results in instruments of different materials delivering a different sound. And of course the design of the windway and fipple will be a big part of how the instrument plays. You might prefer the sound of a thick walled instrument to one with a thin wall.
These factors are just that - factors, to be managed by the designer into a pleasing package. It’s not possible to say this is good and that is bad, you have to consider the whole result. But I would say making a low whistle out of thin walled material allows the designer more freedom in selecting hole sizes and spacings. But they still have to get it right.
So have a look at the instrument you are considering before dismissing it for having a thick wall.