Arguably a BA's greatest contribution, no? Though elicitation, solution assessment, and validation are pretty important too.
Ideation doesn't come easy. It can be costly, and even difficult to quantify. As a Business Analyst, my job is to make sure it's qualified, quantified, and within budget.
Is there a formal process to strategizing? Yes, in fact, there is - and going by your "gut feeling" isn't it.
You might have heard "What Gets Measured, Gets Managed".
I tend to think that neither can happen without the other.
"Yesterday is not ours to recover, but tomorrow is ours to win or lose."
- Lyndon B. Johnson
Are you ready to win?
"Measure what is measurable, and make measurable what is not so." - Galileo Galilei