I recently saw a play version of Sense and Sensibility, and a small thing that happened reiterated one of the points I found odd in other historical dramas: there was a lot of emphasis on being introduced to people before being able to speak with them.
As a specific example, in (this play version of) Pride and Prejudice, Collins, a rector, approaches Darcy, an aristocrat, and others in the scene exclaim "But you haven't been introduced!". In another example, in the fictional series Temeraire by Naomi Novik, set during the Napoleonic wars, the main character finds himself lost in the English countryside, and knows that one of the men under his command is from the area, but finds it unseemly to call on his family's house since they have not ever been introduced, even though he is pretty cold and starving.
What were the rules of being introduced? How rude was it when people approached others without being introduced first? (in modern terms, on a scale of 'not saying bless you when they sneeze' to 'peeing in their face'?)
I think you should re-post this again sometime, as there's likely someone with more knowledge of 19th etiquette and manners who could say something about it. But behind the scene you describe are, like with a lot of Austen's scenes , mechanisms of economics, modes of communication between people of different status and power very common in the 18th century. Darcy is not only noble but rich: he could grant favors, money, quite well have the ability to grant a living, i.e. a church and tithing congregation, to Mr Collins and set him up for life ( or perhaps Mr Collins could already have several livings, have put badly-paid curates to each, and be living a life of leisure off the tithes in London). Mr Collins would normally get an introduction from an intermediary who knows both him and Darcy ( and who might ask Darcy beforehand if he could introduce him), or would bring a letter of introduction from the intermediary to Darcy's secretary and get an appointment, or even simply write Darcy for the same thing. And along with meeting with other people wanting favors Darcy would be prepared to talk to him- or have the option not to meet him at all, or have the secretary write him a letter declining his request. If it was simply a social call, of course ( say, because Collins was a neighbor) , the introduction could be far easier, with Collins perhaps asking one of Darcy's friends right there to introduce him- but the friend would still want to know what it was about, and who Collins was. For Collins to approach him directly, Darcy might have to be having to consider a request without knowing him, or put aside other business that's pressing, etc. and the result might be a public refusal of the request, which would be embarrassing to both. Approached in this way, Darcy might even "cut" Mr Collins: refuse to even acknowledge his greeting, which would be an extremely humiliating thing for Collins, and anyone who has any sense of place ( which of course Collins does not) would avoid this possibility.
On the other hand, if I understand the Napoleonic scene correctly, it seems far-fetched that a soldier could not bring his fellow soldiers to the family house- he could make the introductions himself.