Friendship implies a mutual familiarity which some people may rightly feels needs to be earned rather than simply assumed by one party. While the terms Prince or Princess are intended to elevate the standing of the other party, and doesn't imply any mutual familiarity (just the opposite, in fact.)
If two total strangers meet each other for the first time, I think it is reasonable to assume they haven't yet established mutual "friendship." Unless they both mutually agree to use the term "friend" to address each other, it is presumptuous to do so. And it can feel creepy or even offensive to some people in some situations.
This reminds me of the regional practice for some women in the service industry to call their customers "honey" or "darling." That is also meant as a term of endearment and familiarity by them. I don't mind it when my waitress calls me honey or sweetie. I find it charming and endearing, as intended.
But, if a male waiter did that to my wife, it would be less charming and slightly creepy. If a male colleague did to to a coworker, that would be borderline sexual harassment.
We are all living in the same culture, so we understand what the boundaries are and usually avoid overstepping them. But that doesn't always work: in some regions (and time periods) it was/is perfectly acceptable to call strange females "darling" "honey" and "sweetie." And I can imagine that some wives may find it disturbing for an attractive waitress to call their husband "darling" in front of his family.
Assuming and imposing too much familiarity can sometimes cause offense even if it's intent was entirely positive. And simply assuming that everyone will feel it's "OK" just because you do is not very inclusive or compasionate.
When I was younger, I used to chuckle when folks called me "sir." Now that I've lived long enough to warrant the title, I hope the practice sticks around for a bit longer.
