The problem with this line of thinking is that a piece of software is ultimately built to solve a problem in our real, messy, uncertain world. There is no way to "prove" that an application served its intended purpose. As Fred Brooks wrote: "Even perfect program verification can only establish that a program meets its specification. […] Much of the essence of building a program is in fact the debugging of the specification."
Exactly by the time you could formally prove the application is correct, the market will have moved on to something different. Right now the combination of quick to develop and mostly correct seems to be more desirable to companies then slow to develop and formally correct. The success of languages like JavaScript and python show this.
