Spot on, this is the thing people often miss out.

These problems aren't actual problems in the way most people think about. They are problems in the way that they are exercises. Like the Navier Stokes problem is reporting in the news like one of the biggest problems in maths ever. Leading people to think we are stuck on it and can't progress in some way without a solution. But in reality the limitations of the equation are well known and don't impact normal every day use. And in cases where they would, we have other tools at our disposal.

The goal of these problems is to challenge mathematical people and push boundaries. Having a proof pop out of nowhere is like having someone tell you the answer to a question, where the whole goal was to formulate the answer yourself. The answer itself is meaningless, that's why you get 0 points on the exam unless you show the workings out. It's like having a movie spoiled for you, the goal wasn't to know the outcome, the goal was the experience the story yourself.

Working backwards from some proof might lead to insights, but it also might not and be harder than working forwards. It also might pick a certain path, where there were multiple and we would be blind to the other paths. Those other paths might lead to more insights, if we had explored them.

The way OpenAI specifically has approached this is also very weird and awful in my opinion. Like they set their sights on yet again ruining some aspect of the world with AI and then throwing billions of dollars at it to make sure it's properly ruined. For what purpose exactly? Not to make any money, that's for sure, they are 2 trillion in the hole and counting.

Looks like you have a misunderstanding of what a mathematical proof is. I have but a mere bachelor's in applied mathematics and employed as a statistical engineer for a couple decades now. If a proof is successful at showing a mathematical statement is true, it's a done deal. It doesn't work like science which relies on mathematical models to explain its anecdotes.