On what level do You want to be as a product owner?
This article describes 5 levels of maturity as a product owner.
Then I guess it is up to you (OP) what you are happy with coming from the described situation.
In a globally competitive marketplace there is no place for complacency
With technology providing a global reach from any corner of the globe, you don't know where your next competitor is going to emerge.
Is there always a next step?
Yes, there is. Are you growing? Even if the answer is yes, you could be growing faster. Are you gaining market share? Even ...
In my first superficial reading of this, I'd identify several of these issues as being executive concerns. They're the ones on the bridge, they're the ones that the customer's executives are going to call.
So – in my humble – "product managers" are the folks that these executives are naturally going to turn to, to "actually execute" ...
You always start Customer Development with a vision and an initial strategy as process inputs, but they can and must evolve along with your business model. The Customer Development methodology is intrinsically the search for a validated and repeatable business model. Trying to develop a sustainable business model without an initial vision or strategy ...
If I may, let me very-kindly your words against you:
"Does it make sense to think about it during customer development, in the early stages of a startup? During these stages, we first aim to identify the problem and try to find a solution to reach market-fit in a profitable market."
"Excuse me ... who exactly do you plan to be selling to, if ...
Vision and strategy advances as your company expand. Thinking about and considering customer dev is an essential way to get your priorities straight because there's no such thing as "too early" when building a start-up.
If you don't know what your company is about, you won't be able to provide solution(s) to your customer(s) problem.
Though it may ...
A vision statement as well as strategy is not something static.
As the company evolves the vision and strategy will inevitably evolve.
Thus it makes sense that during customer development, as you understand what the potential customers would want and what you can deliver, your vision and strategy will become clearer, or even change.