I’ve been through the process once, so I’m certainly not an expert.
My guess is that it probably would have been possible. At that point, we’re already under contract (which means our offer has been accepted), and finalizing the loan and home owner’s insurance was part of closing.
The reason I didn’t dig into it too much at the time is I figured that the bank was probably a more sophisticated purchaser than I would have been, especially given the time pressure of needing to make a (reasonably) quick decision.
So I decided that, despite my immense annoyance and not being able to see the homeowners insurance agreement before the closing was complete, that I’d accept the bank’s choice, and use my first year of homeownership to learn the contract and decide if I wanted to change carriers.