As to the iPad and any future tablet computers, there should be no problem supporting WGT on them, because WGT's default game screen is smaller than a tablet's screen anyway. (However, WGT would have to move away from Flash in order to be playable on iOS.)
The trouble with iPhone or any other phone is its small screen. I tried it, like I said, and I couldn't play because of the shot meter being unusable. But even if the shot meter worked, it would be a hassle to play WGT on a phone screen, because you'd have to keep zooming in and out all the time in order to really see what was going on. This means WGT.com would have to completely rework the game for telephone screens, with automatic zooming in and out depending on whatever was currently happening in the game... I just can't see that happening, because WGT's development of the game is extremely slow even on the main platform, they do not seem to have enough staff both on the programmers' and customer support end, etc. Creating a whole new mobile platform for WGT golf would seem like a monumental undertaking under these circumstances. 
(But, it should definitely be pretty easy for WGT.com to let us log in to this site and the forums, at least, when using iPads/iPhones!)