That's just too slow for business in my experience though. Rightly or wrongly, they want it now, not in a couple of sprints.
So what we do is we put both the investigation and the implementation in the same sprint, use the top of the range for the implementation, and re-evaluate things mid-sprint once the investigation is done. Of course this messes up predictability and agile people don't like it, but they don't have better ideas either on how to handle it.
Not sure if we're not enough agile or too agile for scrum.
I think it often depends a lot on who the stakeholders are and what their priorities are. If the particular feature is urgent then of course what you describe is common. But when the priority is to maximize the number of features you're delivering, I've found that the client often prefers to do the bounded investigation and then work on another feature that is better understood within the same sprint, then revisit the investigation results at the next meeting.
But yes -- nothing prevents you from making mid-sprint reevaluations.