I used to think that the tangle of communications at Bree was a bit of a mess on Tolkien’s part. Frodo reminds the Hobbits that he’s going by Underhill, Aragorn overhears this, Aragorn introduces himself, the Hobbit mistrust him, then Barlima remembers Gandalf’s letter.

it would be cool if gaffer was gandalf's spy from the start

It all seems messy and a bit pointless - and, arguably, it is, if you’re judging by narrative flow. It’s not like we have a chapter or three of “can Strider be trusted”. The idea gets raised and dismissed so quickly it seems redundant.