But I don't get their importance and I wish I could somehow frame my project in another way but to create a vision.
I don't want to galvanize with promises about a vision. I'd rather just document what's there and where we're at in the present.
So are there successful projects that have diverged from the classical "problem, vision, mission" statements?
You'll get all sorts of useless advice about demonstrating traction, about your team and about the projected market size but those things are generally used to let you down easy when an investor takes a pass. The traction isn't big enough or is too niche, your team is missing some key element, your market size assumptions are wrong.
The reality is the investor doesn't understand what you are doing, why you are doing it or how you propose to scale from your first customers.
Thats where vision is important. If you can't explain it, you don't know why you are doing something and you don't know how you are going to scale.
If you don't know that stuff, your investor doesn't know what you will be spending their money on.
The problem, vision, mission, statement helps you as much as external parties evaluating your products potential including customers.
Just get it done.
Basically, the CEO makes it clear what they want to do and what success looks like. (Mission, vision)
But they also break that down into measurable things. The people doing the job can say stuff like our goal/mission is to do X. To do X, we need ABC. My job is doing C, and it's measurable when c0 and c1 happens.