I have one of Colin's "modal" D whistles, one of the first few he made. It doesn't have a thumbhole for the C-nat, but it has 7 holes on top of the instrument, so you can get C natural (in both octaves) by stopping the last holed with your bottom-hand little finger. And it has an F-natural thumbhole on the back.
I experimented seriously with it for a while. The possibilities were very intriguing - C natural had a nice strong tone, I could do rolls on F natural, crans on C natural if I remember correctly, and certain difficult passages or tunes became feasible or easier. But I didn't stick with it. The thumbhole wasn't in a natural position (hehe) and I ended up taping over it.
Regarding the weak sound of C natural on a standard whistle, the need to cross-finger in various ways depending on the whistle, and the fact that what rolls you can do on that note are a trifle unconvincing... well, yes, that's a limitation of the instrument. Or a feature of it, the nature of the beast, depending on your point of view. Working with an instrument's limitations is OK with me.
If you don't, what do you ultimately end up with? A Boehm-system flute, that's what.
(Which is fine, of course, if you have to play in an orchestra, jazz combo, or wind band - before all the Boehm-system players start beating me to a pulp.)
PS Here is a review of the modal whistle - from 11 years ago, oh dear Lord. viewtopic.php?f=1&t=664&start=0