OK, but here's the thing. I don't see how "the gaming supplement explicitly says X, but the mention per book count suggests, to me, Y, so Y is probably true" is a valid interpretation.
If the book says they are common, leave their home a lot to explore, trade with other nations, that people in various places don't think twice about seeing them, etc, then that is the case in the official setting. Even if they're never mentioned again, it remains the case. How frequently supplements and novels mention them is completely irrelevant unless it's all we have to go on. But it isn't. We have direct statements in official material saying that DB are not an astonishing sight, they do leave their home frequently, and they do have a strongly positive reputation, and DB who serve evil organizations are incredibly rare.
Those statements trump extrapolated conclusions from mention frequency.
Except the books never explicitly says they are common.
'They sometimes send small groups of elite warriors to track down known lairs of powerful dragons.'
--->The key word for me is sometimes, and also the fact that they are tracking down dragon lairs, not involving themselves in societies.
'Despite Tymanther's desire for friendly relations with others, it has one few true allies.'
'Unfortunately for them, the strangeness of their customs and their uncertain origins casts many suspicions on the dragonborn and their motives, making establishing long-lasting alliances a challenge. '
'For a time, the dragonborn of Tymanther sought to integrate with their new world while maintaining their own traditions and culture. These efforts gave the nation and its people a reputation for being honorable and worthy of respect... the remaining dragonborn in Faerun now find they must work even harder and with fewer resources to find their place among the people the world.'
'...everyone stares at her because of her white dragon heritage.'
--->All statements indicating that dragonborn have difficulty fitting in with societies other than their own.
'Dragonborn who achieve fame abroad are celebrates as state heroes back in Tymanther. The dragonborn see these few as emissaries of their race, proving to the wide continent of Faerun that they have nothing to fear from dragonborn.'
'Some of Tymanther's dragonborn have spread across Faerun and gained reputations at competent, highly sought-after mercenaries.'
--->The first doesn't indicate how many, the second says 'some.' Not many, not they are common, just some.
As for the Dalelands comment from an adventure:
'Dragonborn, Tieflings, and Others: In general "these races aren’t from around here" People in the Dales are used to seeing outlandish foreigners wander through and so they rarely give such individuals notice.'
This is just an indication that people in a specific location feel this way. Not the continent as a whole. This is in regards to a populace that has been through a lot, and that include among their populace some of the most famous and powerful adventurers in recent history. Described as rustic and xenophobic, but also recognize that skilled adventurers are their first line of defense.
It's also directly contradicted by the 'everyone stares at her' and 'the strangeness of their customs' comments noted earlier.
So perhaps dragonborn would fit best there.
In addition, the majority of mentions or published NPCs are tied to the Cult of the Dragon, which I would consider an evil organization.
I think that the number of times a race appears in a published sourcebook or adventure has some impact if the criteria is whether they are common or not. In those same books there are a great many more humans and elves described especially. One can easily surmise that if there are a lot more humans and elves identified and detailed, that there are more humans and elves.
More importantly, the vague and/or contradictory statements, combined with their low frequency leaves the interpretation to the DM and what they decide works in their campaign. At best, there are as many statements indicating they have difficulty in society as there are that they don't. They are sometimes sought after as mercenaries, but that could be in part because of their appearance, and doesn't indicate that they fit well into society. Just that they are recognized for their combat prowess, and perhaps loyalty.
So I'm not extrapolating conclusions, the conclusion that they are not common is based on what was written, with the frequency, or lack thereof, supporting it. That's not to say that it's not possible to come to another conclusion. It's not 'wrong' that you feel otherwise. It's just that the 'evidence' is presented in such a way that multiple directions are reasonable and possible.
Ilbranteloth