The "almost all of the mobile" part is really bad, and exactly resembles the IE situation on the desktop before. I hope Mozilla will shift the balance there again.
The problem with saying "Webkit is the new IE" is that IE was allowed to stagnate because it was a singular browser with a dominate position in the market. When that position was achieved, it was no longer necessary for the company maintaining it to continue to compete.
Webkit, in contrast, isn't controlled by any one company. The people using it have access to the source, and more often that not are contributing to the project themselves.
I don't think the competition is going to end, It's just going to change form.
Stagnation was only one aspect of the problem. Another big aspect was common bad quality of sites created with IE only in mind. The same often happens with WebKit on mobile.
Webkit, in contrast, isn't controlled by any one company. The people using it have access to the source, and more often that not are contributing to the project themselves.
I don't think the competition is going to end, It's just going to change form.